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DESIGN AND CONSTRUCTION OF A
RADIO TELESCOPE FOR UNDERGRADUATE RESEARCH
A senior thesis submitted to the faculty of
in partial fulfillment of the requirements for the degree of
Bachelor of Science
Department of Physics
Copyright c⃝ 2011 Christopher Stathis
All Rights Reserved
of a senior thesis submitted by
This thesis has been reviewed by the senior thesis committee and the depart-ment chair and has been found to be satisfactory.
Date Dr. Bruce Thompson, Advisor
Date Dr. Matthew Price, Advisor
Date Dr. Matthew C. Sullivan, Senior Thesis Instructor
Date Dr. Beth Ellen Clark Joseph, Chair
DESIGN AND CONSTRUCTION OF A
RADIO TELESCOPE FOR UNDERGRADUATE RESEARCH
Department of Physics
Bachelor of Science
Radio telescopes provide a practical and economical alternative to optical ob-
servatories for astrophysics research and education at primarily undergraduate
physics and astronomy institutions. We have developed an inexpensive radio
telescope capable of observing at Ku Band and L Band frequencies. The
telescope consists a three-stage superheterodyne receiver on custom circuit
boards mounted on a 3 meter parabolic antenna. Software for data collection
and hardware interfacing has been developed in MATLAB. We expect the
telescope to be capable of drift continuum observations of the Sun and Milky
Way at 3cm wavelengths. It can also be easily adapted to measure spectral
emission of neutral hydrogen and OH masers at 1.5 GHz frequencies. I present
our design methods for the radio frequency receiver and printed circuit boards
as well as a discussion of viable celestial sources of radio emission.
The completion of this project would not have been possible without gen-
erous support from the faculty and students in the Ithaca College community,
especially my advisors Dr. Matthew Price and Dr. Bruce Thompson, whose
wonderful encouragement and infinite patience made the monumental task of
preparing a research thesis manageable and rewarding. I’d also like to thank
Dr. Dan Briotta for his cooperation as the gatekeeper of Ford Observatory,
Dr. Luke Keller for sharing his time and his connections at Cornell, and my
Senior Thesis II instructor Dr. Matthew C. Sullivan for his unwaveringly high
A number of financial contributions also helped to make this radio telescope
a reality. I extend my gratitude to Kathy Schaufler for her donation of the
satellite dish that has become our antenna. Special thanks also go to Orbital
Research, specifically their CEO Mike Stevens, for his donation of a bias tee
that is being used to supply power to our receiver. I also acknowledge the
DANA program for a stipend which enabled me to work on the telescope full
time over the Summer of 2009.
Finally, thanks to Jennifer Mellott for her help and patience in the labora-
tory, Nate Porter ’11 and Tori Roberts ’12 for helping to retrieve the satellite
dish, Jon White ’11 for helping with illustrations, and Laura Spitler of Cor-
nell University for sharing her knowledge and her access to radio electronics
Table of Contents vii
List of Figures ix
1 Introduction 11.1 A Brief History of Radio Astronomy . . . . . . . . . . . . . . . . . . 2
1.1.1 Jansky Merry-Go-Round . . . . . . . . . . . . . . . . . . . . . 21.1.2 Reber Sky Survey . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Important Discoveries By Radio Astronomers . . . . . . . . . . . . . 41.2.1 Non-Thermal Radiation . . . . . . . . . . . . . . . . . . . . . 41.2.2 Cosmic Microwave Background . . . . . . . . . . . . . . . . . 61.2.3 Galactic Supermassive Black Hole . . . . . . . . . . . . . . . . 7
1.3 Modern Uses For Radio Telescopes . . . . . . . . . . . . . . . . . . . 7
2 Theory 92.1 The Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . . 92.2 Quantifying Radio Observations . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Flux Density of a Radio Source . . . . . . . . . . . . . . . . . 112.2.2 Blackbody Temperature . . . . . . . . . . . . . . . . . . . . . 13
2.3 Radiation Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.1 Bremsstrahlung . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Cosmic Sources of Radio . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.1 The Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.2 Neutral Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.3 The Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Radiometer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5.1 Superheterodyne Model . . . . . . . . . . . . . . . . . . . . . 272.5.2 Frequency Mixing . . . . . . . . . . . . . . . . . . . . . . . . . 282.5.3 Square Law Detection . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Radiometer Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Design and Implementation 353.1 Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.1.2 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Superheterodyne Receiver . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 Ku Band Low Noise Block . . . . . . . . . . . . . . . . . . . . 373.2.2 L Band Frequency Mixer and Local Oscillator . . . . . . . . . 423.2.3 Filter-Amplifier Stages . . . . . . . . . . . . . . . . . . . . . . 433.2.4 Detector Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2.5 Printed Circuit Board Design . . . . . . . . . . . . . . . . . . 48
4 Results and Testing 534.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 Receiver Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Conclusions and Future Work 575.1 First Expected Observations . . . . . . . . . . . . . . . . . . . . . . . 575.2 Longterm Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Appendix A Matlab Script 61
List of Figures
1.1 Data taken by Jansky’s Merry-Go-Round. . . . . . . . . . . . . . . . 31.2 Photograph of the Reber parabolic antenna. . . . . . . . . . . . . . . 51.3 Plot of the Cosmic Microwave Background. . . . . . . . . . . . . . . . 7
2.1 Diagram of the electromagnetic spectrum. . . . . . . . . . . . . . . . 102.2 Plot of the solid angle. . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 The blackbody energy distribution. . . . . . . . . . . . . . . . . . . . 142.4 Diagram of a bremsstrahlung interaction. . . . . . . . . . . . . . . . . 162.5 Diagram of synchrotron radiation. . . . . . . . . . . . . . . . . . . . . 212.6 Plot of synchrotron observations demonstrating the spectral index. . . 242.7 Radio spectrum of the Sun. . . . . . . . . . . . . . . . . . . . . . . . 322.8 Block diagram of a superheterodyne receiver. . . . . . . . . . . . . . . 33
3.1 Block diagram of the complete radio telescope. . . . . . . . . . . . . . 383.2 Schematic of the RF receiver circuit. . . . . . . . . . . . . . . . . . . 393.3 Schematic of the IF detector circuit. . . . . . . . . . . . . . . . . . . . 403.4 Diagram of the LNB multiplexer. . . . . . . . . . . . . . . . . . . . . 423.5 Bode plot of the image rejection mixer. . . . . . . . . . . . . . . . . . 453.6 The Sallen-Key filter topology. . . . . . . . . . . . . . . . . . . . . . . 463.7 Plot of experimental gain for 4-pole Butterworth filter. . . . . . . . . 473.8 Heating profile for reflow soldering. . . . . . . . . . . . . . . . . . . . 493.9 PCB schematic of the RF receiver board. . . . . . . . . . . . . . . . . 503.10 PCB schematic of the detector circuit. . . . . . . . . . . . . . . . . . 51
4.1 Results of testing the receiver with a microwave source. . . . . . . . . 554.2 Measurement of the intrinsic noise of receiver PCBs. . . . . . . . . . . 56
Before the 20th century, astronomers possessed a limited toolset with which to observe
the sky. The whole of our knowledge concerning objects in space was derived from
the visible light we observed. Methods for detecting infrared light were eventually
developed, but large gaps in our understanding still remained. Since Maxwell’s work
in the 1860s, scientists knew that electromagnetic radiation could occur at any wave-
length, yet the efforts of physicists such as Nikola Tesla to observe unconventional
frequencies of radiation coming from space were consistently met with failure .
The first person to successfully observe radio frequency light from space, Karl Jan-
sky, did so by accident. His discoveries led to a revolution in astrophysics. Through
World War II and into the 1960s, research in radio astronomy exploded, and the
results challenged fundamental theories about the nature of the universe. The newly
discovered abundance of radio emission in the universe did not agree with scientists’
understanding of radiation. Radio telescopes also provided the means to detect new
and exotic classes of celestial bodies. Radio astronomy has been responsible for many
important discoveries since its inception, such as the measurement of the cosmic mi-
crowave background and its anisotropy. Today, astrophysicists use radio telescopes
2 Chapter 1. Introduction
for a variety of applications, including monitoring the sun for sunspots, studying the
atmosphere and ionosphere of planets in the solar system, and seeking out extrater-
1.1 A Brief History of Radio Astronomy
1.1.1 Jansky Merry-Go-Round
In 1931, Bell Laboratories commissioned a project to study the causes of poor signal
quality in shortwave radio communications, specifically those due to fluctuating iono-
spheric and atmospheric conditions. A young American physicist named Karl Guthe
Jansky was hired to carry out the research. To monitor the air for these noise signals,
Jansky constructed a directional antenna spanning 30 meters in diameter. He steered
the device by rotating it along a circular track, which earned it the nickname of ”Jan-
sky’s Merry-Go-Round.” He detected and categorized three types of noise signals in
his first months of observations - lightning strikes, automobile ignition sparks, and
a slowly oscillating hiss. A sample of Jansky’s data, recorded by pen and paper, is
depicted in Fig 1.1. By mid 1932, this slow oscillation was the only noise that Jansky
could not explain, and it became the focus of his research. By holding the antenna
in one place for several weeks at a time, Jansky determined that the source drifted
across the sky with a steady period of 24 hours. Based on this, he hypothesized that
the Sun was the source of the signal. To confirm this, he sought to observe it during
the total solar eclipse of August 31, 1932 . Evidence that the signal changed when
the Sun was blocked would confirm this hypothesis. Jansky’s data from this solar
eclipse revealed no measurable effects. This forced Jansky to seek out other possible
explanations. The astrophysicists who he consulted about this problem realized that
the precise period of oscillation was 23 hours and 56 minutes, the length of a sidereal
1.1. A Brief History of Radio Astronomy 3
Figure 1.1 A plot produced by Jansky’s directional antenna. Jansky at-tributed the pulses seen in this image to electrical storms and automobileignition sparks, but could not immediately explain the slow background os-cillation. This was later determined to be emitted by the center of the MilkyWay galaxy. (Source: )
day. This showed that the noise source must lie somewhere in space. In his pursuit
of atmospheric noise observations, Jansky had serendipitously produced the first evi-
dence that measurable radio frequency signals are emitted by celestial bodies . He
continued to monitor this signal, and in 1933 concluded that it was strongest when
his antenna was pointed at the constellation Sagittarius. Optical telescope images
of the same region of the sky confirmed that the source of the radiation was at the
center of the Milky Way Galaxy . This result was well received by astronomers,
but did little to answer the question that Jansky was tasked by Bell to answer. As a
result, his project was discontinued in 1934. While he made efforts to pursue further
research on his own time, illness and financial problems prevented him from making
significant progress .
1.1.2 Reber Sky Survey
It was not until 1937 that an amateur radio astronomer, Grote Reber, made efforts to
continue Jansky’s work. In the midst of the Great Depression, Reber applied to work
at Bell Labs alongside Jansky, but was turned away. In response, he constructed his
4 Chapter 1. Introduction
own radio antenna in his backyard - a parabolic dish 9 meters in diameter, not unlike
the antennas used for modern radio telescopes today. An image of the telescope is
depicted in Fig 1.2. Reber mounted his dish on a tilting stand so he could steer it along
the altitudinal direction. He developed several receivers for the telescope operating
at a variety of frequencies. The one to produce the most useful data operated at 160
MHz . Reber used this telescope to perform a survey of the 160 MHz radio sky
in 1941, earning him publications in several astrophysical journals . The survey
raised questions about the nature of the universe, specifically drawing attention to the
abundance of low frequency radiation emitted in space . Reber reached celebrity
status in the astrophysics community for his work, leading major observatories to
adopt their own radio astronomy research programs.
1.2 Important Discoveries By Radio Astronomers
1.2.1 Non-Thermal Radiation
The abundance of low frequency radiation in space demonstrated by Reber’s survey
came as a surprise. Scientists at the time believed that radiation in space occurred
only as blackbody radiation. They suspected that given the high temperature of stars,
most radiation in space would be observed at frequencies around the visible spectrum
where their blackbody radiation is most intense . The Reber sky survey was the
first empirical result to suggest that this was not the case. Blackbody radiation
does not account for the intensities of radio frequency radiation Reber observed .
Some other previously unknown mechanism was responsible. The study of these
unexplained emission modes led to the observation of synchrotron radiation, thermal
bremsstrahlung, atomic and molecular spectral emission, and other modern physical
1.2. Important Discoveries By Radio Astronomers 5
Figure 1.2 A photograph of the parabolic radio antenna used by Grote Reberto conduct a survey of the radio sky in 1941. The telescope was 9 metersin diameter and featured an altitudinal steering mechanism. Reber’s resultsdrove scientists to pursue further radio astronomy research throughout themid-20th century. (Source: National Science Foundation (public domain))
6 Chapter 1. Introduction
1.2.2 Cosmic Microwave Background
Most radiation at radio frequencies is non-thermal in nature. RF blackbody radiation
is present in the universe but has intensity peaks at cold temperatures (less than 50
Kelvin) . As a result, blackbody radiation emitted by hot objects like stars is
negligibly weak at RF - their spectrum is dominated by other mechanisms. However,
theoretical models predicted the temperature of the interstellar medium (ISM) to be
sufficiently cold for blackbody peaks to occur at a low frequency. The temperature
of the ISM could be determined by measuring this peak. In 1955, French astronomer
Emile Le Roux performed a sky survey at a frequency of 900 MHz and discovered
that the ISM emits a nearly isotropic, persistent background radiation peaking at a
temperature of 3K ± 2K . Ten years later, American astronomers Penzias and
Wilson confirmed this measurement to a greater degree of precision, and earned the
Nobel Prize in Physics in 1978 for their efforts . The significance of the thermal
radiation in empty space, referred to as the cosmic microwave background radiation
(CMBR), is in its implications to cosmology. Its existence supports the Big Bang
theory which has become the standard model for the first moments of the universe.
The model states that while the universe was sufficiently hot, it consisted of free
electrons and nuclei which continuously absorbed and re-emitted photons. As the
universe expanded, the temperature fell to a point where electrons and protons could
bind to form atoms. These atoms did not absorb all photons in the way that free
particles did, so this transition left behind a collection of photons which had been
emitted by particles but not re-absorbed . The energy observed in the CMBR is a
direct observation of these photons which continue to propogate through space. An
image of the CMBR is depicted in Fig 1.3.
1.3. Modern Uses For Radio Telescopes 7
Figure 1.3 An image of the cosmic microwave background radiation pro-duced by the Wilkinson Microwave Anisotropy Probe in 2010. The cosmicmicrowave background provides strong evidence for the Big Bang theory. Ofcurrent interest to cosmologists is the anisotropic distribution of the radia-tion, which is clearly seen here. (Source: )
1.2.3 Galactic Supermassive Black Hole
The radio source at the center of the Milky Way first detected by Jansky is known as
Sagittarius A*. Radio and X-ray observations of this region suggest that the source
has an angular diameter of 37 microarcseconds and is positioned near a supermassive
black hole. Gravitational lensing models confirm that the radio source is not the center
of the black hole itself, but the blackbody radiation produced by matter heating to
extreme temperatures as it accelerates near the event horizon . The discovery
that our galaxy has a black hole at its center was made possible by radio astronomy.
1.3 Modern Uses For Radio Telescopes
A variety of research questions are being addressed by radio astronomers today. Cos-
mologists are interested in the ansiotropy of the cosmic microwave background due
8 Chapter 1. Introduction
to its implications to the general theory of relativity and the early history of the
universe. For example, the observed anisotropy of the CMBR was used to determine
that the Milky Way galaxy is traveling at 22 km/s with respect to the rest frame of
the ISM . More applied uses for radio astronomy include the observation of sunspot
population at the Solar and Heliospheric Observatory, as well as the study of Earth’s
ionosphere, currently being conducted by the National Astronomy and Ionosphere
Center at Arecibo Observatory. Astronomers are also using radio to observe distant
objects such as quasars, pulsars, and supernova remnants by interferometry at obser-
vatories like the Very Large Array, which consists of 27 independent antennas .
2.1 The Electromagnetic Spectrum
Radio frequency radiation is a specific type of electromagnetic (EM) wave. EM waves
have a frequency proportional to the total energy that they carry. This is described
by the Planck-Einstein equation 
E = hν (2.1)
where E is the total energy in joules, h is Planck’s constant, and ν is the frequency in
Hertz. The full range of possible frequencies makes up the electromagnetic spectrum.
This spectrum is divided into categories as seen in Fig 2.1. The radio spectrum is
divided further into several bands. The designations developed by the Institute of
Electrical and Electronics Engineers (IEEE) are depicted in Table 2.1.
10 Chapter 2. Theory
Figure 2.1 Diagram of the electromagnetic spectrum, with frequency in-creasing from left to right. Radio and microwave frequency radiation makeup the lowest frequencies, and as a result of Eq 2.1, the lowest energies.
Table 2.1 IEEE frequency band designations for the radio spectrum.
Band Frequency Range Nomenclature
HF 3 to 30 MHz High Frequency
VHF 30 to 300 MHz Very High Frequency
UHF 300 to 1000 MHz Ultra High Frequency
L 1 to 2 GHz Long Wave
S 2 to 4 GHz Short Wave
C 4 to 8 GHz Compromise between S, X
X 8 to 12 GHz Crosshair (WWII Fire Control)
Ku 12 to 18 GHz Under Kurz
K 18 to 27 GHz Kurz
Ka 27 to 40 GHz Above Kurz
V 40 to 75 GHz -
W 75 to 110 GHz -
mm 110 to 300 GHz mm Wavelengths
2.2. Quantifying Radio Observations 11
2.2 Quantifying Radio Observations
2.2.1 Flux Density of a Radio Source
A radiation source in the sky has some apparent size described by its solid angle Ω.
The solid angle is a two dimensional angle that resolves an area segment of a sphere.
This is analogous to a one-dimensional planar angle which resolves the arc length of
a segment of a circle. The solid angle in spherical coordinates is
dΩ = sin θdθdϕ (2.2)
The unit of the solid angle is the steradian (sr.) Integration over all solid angles gives
the surface area of the sphere of radius r, as seen in Fig 2.2. Radiating bodies can be
described according to their emitted power per unit area, or flux. The basic unit of
radiated energy, the monochromatic intensity I(ν), is defined as the flux per unit solid
angle at a specific frequency. It has units of J m−2s−1Hz−1sr−1. Radio astronomers
most commonly characterize sources in terms of their monochromatic flux density,
which is the monochromatic intensity integrated over the solid angle.
The flux density S has units of Wm−2Hz−1, but in radio astronomy the conventional
unit of flux density is the Jansky , defined as 10−26Wm−2Hz−1.
Measuring the flux through a solid angle of the sky is the fundamental task of a
radio telescope. The resolution of the telescope is described by the size of this solid
angle, called the beamwidth. A high resolution corresponds to a small beamwidth.
Astronomers use calibration techniques to determine the beamwidth of a telescope so
that the flux density of a source can be calculated from a measurement of flux.
12 Chapter 2. Theory
yFigure 2.2 The solid angle is a two-dimensional angle which describes thesurface area of a section of a sphere. Integration over all solid angles givesthe area of a sphere of radius r. The size of this solid angle is also referredto as the beamwidth of the telescope. Telescopes with a solid angle of Ω canresolve features of celestial bodies that appear larger than Ω in the sky.
2.2. Quantifying Radio Observations 13
2.2.2 Blackbody Temperature
Prior to the mid 20th century, astrophysicists believed that all radiated energy from
celestial bodies was due to blackbody radiation. This is a specific mechanism of
emission in which the monochromatic intensity is dependent on the temperature of
the body being studied. The intensity emitted at a given frequency ν by an ideal
blackbody is expressed mathematically by Planck’s Law, given as 
Bν(T ) =2hν3
This quantity is known as the monochromatic intensity because it refers to the inten-
sity at one frequency. A plot of the energy emitted by a blackbody as a function of
frequency for a variety of temperatures is shown in Fig 2.3.
Since RF radiation is of low frequencies, hν << kT except in the case that T is
very small. For sufficiently large values of T, the exponential term in Eq 2.4 reduces
The regime where hν << kT is known as the Rayleigh-Jeans regime because Planck’s
Law reduces to the Rayleigh-Jeans Law 
Bν(T ) =2ν2kT
Monochromatic intensity increases linearly with temperature within this regime. When
hν ∼ kT , the Rayleigh-Jeans Law breaks down and Planck’s Law must be used for
accurate calculations. At Ku band frequencies, this breakdown occurs near a tem-
perature of 1 K. This means that for blackbodies of a temperature above 1 K the
Rayleigh-Jeans Law is sufficient for predicting their radiation spectrum at Ku Band.
The temperature of a blackbody is calculated by solving Eq 2.6 for T , which yields
T =Bν(T )c2
14 Chapter 2. Theory
Figure 2.3 Log-log plot of the energy distribution produced by blackbodyradiation. Notice that the intensity goes as the square of the frequency withinthe Rayleigh-Jeans Limit, which breaks down at frequencies far outside theradio spectrum. The point of maximum intensity is a function of the black-body temperature, given by Wien’s Displacement Law, which increases infrequency as the temperature increases. Source: 
2.3. Radiation Mechanisms 15
This equation will not necessarily hold to great degrees of precision for real objects
since it is derived only for ideal blackbodies. However, it describes the temperature
an ideal blackbody would have if its monochromatic intensity is measured as Bν . This
temperature is known as the brightness temperature and is widely used to discuss the
radio emission of real sources .
2.3 Radiation Mechanisms
Comparing empirical observations of intensity at RF to the intensities predicted by
the Rayleigh-Jeans Law reveals some discrepencies. For example, if the Sun were con-
sidered a perfect blackbody, the Rayleigh-Jeans law implies that it has a temperature
of 100,000 K at a frequency of 1.4 GHz. Measurements of the Sun at visible frequen-
cies give a temperature of approximately 6000 K . This discrepency implies that
blackbody radiation is not the only source of radiation emitted by the Sun. Most of
these other sources of radiation were not well understood until the mid 20th century.
Radiation from stars such as the sun and insterstellar ionic clouds such as those found
in the Milky Way is often a result of charged particles such as electrons experienc-
ing acceleration due to the presence of ions. This interaction is known as thermal
bremsstrahlung or free-free radiation. In the most common case it consists of elec-
trons interacting with hydrogen ions in a plasma. A region of space occupied by a
high density of hydrogen ions is called an HII region .
Consider a single electron interacting with a single H+ ion. The particles feel a
force governed by Coulomb’s Law. In collisions, strong forces are generated which
typically produce radiation in the X-ray frequencies. The energy of X-ray photons
16 Chapter 2. Theory
Figure 2.4 Diagram of a bremsstrahlung interaction. Electrons acceleratingdue to the presence of ions emit radiation according to Larmor’s formula.These interactions are characterized by the impact parameter b which de-scribes the minimum distance between the charges throughout the interac-tion.
is much higher than that of radio photons. For this reason we are only interested in
weak interactions, i.e., an electron passing by an H+ ion. The forces on the particle
during an interaction are described in terms of the distance between the particle and
the ion, l, and the impact parameter, b. The impact parameter is defined as the
minimum value of l throughout the interaction. When b = l, the particle feels the
strongest force, as shown in Fig 2.4. The force felt by the particle can be separated
into components parallel and perpendicular to its velocity
In either case the acceleration causes the particles to emit radiation according to
Larmor’s formula 
2.3. Radiation Mechanisms 17
where P is the radiated power, q is the charge, and v is the acceleration of the particle.
A complete investigation of bremsstrahlung should consider the radiation from both
forces, however it is known that the parallel component produces radiation outside of
the radio range, so for the purpose of this discussion we study only the perpendicular
component . Bremmstrahlung from one interaction is better described as an
event rather than a sustained signal. A single pulse of radiation is produced by the
electron, which we approximate as a gaussian distribution . Fourier analysis of
this distribution suggests that the maximum frequency of radiation resulting from
the interaction is 
ω ≈ v
which lies well into the infrared range in most cases.
Now consider a region of space populated by a hydrogen ion plasma. The average
velocity of the electrons depends on their average energy, or the temperature of the
plasma. The predicted range of values for the impact parameter b depends on the
density of the plasma. Assuming the region is in thermal equilibrium, the electrons
and ions have equal average kinetic energy, but since the ions are many orders of
magnitude more massive, we assume they remain stationary. The monochromatic
intensity of radiation can be written in terms of the emission coefficient, which is
or the total flux per unit volume per unit solid angle at a frequency ν. It has units
of J m−3s−1Hz−1sr−1. From this we write
Ib = 4πϵν (2.13)
where ϵν is the emission coefficient and the factor of 4π is a result of integration over
18 Chapter 2. Theory
For a specific range of impact parameters bmin → bmax, and electron and ion
densities given by Ne and Ni, this emission coefficient is given by 
Detailed derivations of this coefficient can be found in advanced thermodynamics
texts such as ref .
Ultimately we are interested in the spectral index for bremsstrahlung distributions.
The spectral index is a unitless quantity that describes the frequency dependence of
the total flux emitted by a source. It is the slope of the intensity plotted as a function
of frequency in a log-log plot. (Unfortunately there is no accepted sign convention
for the spectral index so a positive index could imply a positive or negative slope
depending on the context. Throughout this report a positive spectral index is taken
to imply a positive slope.) We assume that the particles which make up the source
have a power law energy distribution 
N(E)dE ∝ E−δdE (2.15)
where N is the number of particles per unit volume with energies between E and
E + dE, and δ is a positive constant.
To calculate the spectral index we will need the maximum and minimum values
of the impact parameter that give rise to radio frequency radiation. The impulse on
the passing electron due to the field of the ion is
Again we are only interested in the perpendicular component of force, so we take the
perpendicular component of the electric field E⊥ = E cos θ. Recalling Eq 2.9, we may
2.3. Radiation Mechanisms 19
By applying a change of variables dt = b/v sec2 ϕδϕ, this becomes
Since the momentum transfer is inversely proportional to the impact parameter, we
can solve for the minimum value of b in the case where ∆P is as large as possible.
This occurs for a perfectly elastic interaction where the change in momentum is twice
that of the initial momentum of the electron, or
∆Pmax = 2mev (2.19)
From this we see that the minimum value of the impact parameter is 
and recalling Eq 2.11,
From these results we can calculate how much of the radiated energy will be re-
absorbed by the plasma (so not transmitted to Earth), described by the absorption
coefficient. The absorption coefficient κν is given by Kirchoff’s Law 
Substituting for ϵν and applying the Rayleigh-Jeans Law for Bν(T ), we have
κν ∝ 1
within the Rayleigh-Jeans regime. With this value of the absorption coefficient, we see
that the flux density goes precisely like the flux of a blackbody, with a spectral index
20 Chapter 2. Theory
of α = 2. This is why astronomers call this interaction “thermal bremsstrahlung.” As
frequency increases beyond 10 GHz, the flux density decreases slowly with frequency
and has a spectral index of α = −0.1 in HII regions .
2.3.2 Synchrotron Radiation
Synchrotron radiation makes up most of the radiation in space which cannot be ac-
counted for as blackbody radiation or bremsstrahlung . It is produced by electrons
in strong magnetic fields moving at relativistic speed. Scientists first observed it in
the laboratory as an unwanted source of energy loss in a circular electron accelera-
tor . The trajectory of an electron in a uniform, static magnetic field forms a helix.
Particles undergoing circular motion are constantly accelerated in the direction per-
pendicular to the motion. This is illustrated in Fig 2.5. The angular velocity of this
circular motion ωC is called the angular cyclotron frequency. The angle between the
direction of velocity and the magnetic field line is the pitch angle θ. Cyclotron fre-
quency is a function of the field strength B, the charge q, the mass m0. Accounting
for relativistic speed, it is given as 
, νC =qB
where γ = 1/√
1 − (v/c)2 is the Lorentz factor in special relativity. The synchrotron
radiation of one particle is sharply peaked at a specific frequency. For this reason our
model assumes that all synchrotron radiation produced by this particle will occur at
one frequency called critical frequency ν, which for ultrarelativistic particles is given
ν = γ2νC (2.26)
Radiation from a particle moving in this manner will be observed as a series of pulses
occurring at a regular interval. This is because synchrotron radiation will only be
2.3. Radiation Mechanisms 21
(proton or electron)
Figure 2.5 An illustration of synchrotron radiation. Charged particles movein a spiral pattern when subject to a strong magnetic field. The resultingacceleration causes them to emit radiation at the cyclotron frequency.
22 Chapter 2. Theory
detected when the direction of the particle’s velocity is in the observer’s line of sight.
For the same reasons it is also sharply polarized.
We are ultimately interested in the power radiated by a celestial body due to
synchrotron radiation. Relativistic electrodynamics  describes the energy lost by
a single relativistic particle moving in a spiral trajectory as
sin2 θ (2.27)
for a specific pitch angle θ. This can be rewritten in terms of the magnetic energy
and in terms of the Thomson cross-section, a constant defined as
so we are left with
P = 2σTβ2γ2cUB sin2 θ (2.30)
where β = v/c. To describe an ensemble of particles of synchrotron radiation we
are interested in the value of their spectral index. To calculate this we will need the
emission coefficient. We can write
ϵνdν ≈ −dE
since the power emitted is the time derivative of the emitted energy. In this case the
energy E is the energy of the individual relativistic electrons, given by E ≈ γmec2.
Substituting these expressions and applying some clever algebra we arrive at
ϵν ∝ B(δ+1)/2ν(δ−1)/2 (2.32)
From this the spectral index can be extracted
P (ν) ∝ ν(−δ+1)/2 (2.33)
2.4. Cosmic Sources of Radio 23
The exponent on the frequency ν is the spectral index. The value of δ for RF syn-
chrotron emission between 1 GHz and 100 GHz in our galaxy has been empirically
measured as 2.4 . In this frequency regime, the spectral index has a value of −0.7,
as shown in Fig 2.6. This result shows that the spectrum of a synchrotron source
follows a different distribution than the blackbody curve, which has a spectral index
of 2 since in the Rayleigh-Jeans regime the energy is proportional to ν2. Furthermore,
the flux from a synchrotron source is a relatively strong function of frequency, so we
can expect the strongest levels of synchrotron radiation to be emitted at the lower
frequencies of the power law regime - between 1 and 10 GHz.
2.4 Cosmic Sources of Radio
The strongest sources of RF radiation as observed from Earth are the Sun and the
Milky Way. Both of these sources produce a complicated mixture of radiation mech-
anisms for which there are a variety of models. Their emission can be measured
even with the most insensitive radiometers, so they are suitable targets for the first
measurements taken with a new telescope. In addition to the Sun and Milky Way,
the spectral line of neutral hydrogen molecules is easily accessible. This is due to the
abundance of hydrogen throughout the universe.
2.4.1 The Sun
Solar RF radiation is classified into four components: “quiet Sun” emission due to
plasma bremsstrahlung, a slowly-varying component of synchrotron radiation and
bremsstrahlung due to the magnetic fields trapped by sunspots, synchrotron radia-
tion from electrons in short-lived noise storms, and wideband synchrotron emission
from short radio bursts associated with solar flares . The range and relative inten-
24 Chapter 2. Theory
Figure 2.6 Summary of observational synchrotron radiation data demon-strating the negative spectral index throughout most of the radio spectrum.This shows that synchrotron radiation is fundamentally different than black-body radiation and follows a different distribution of energy. Source: 
2.4. Cosmic Sources of Radio 25
sities of these signals are summarized in Figure 2.7. At Ku Band, the slowly-varying
component which depends on sunspot population is accessible. Monitoring this com-
ponent is a technique used by NASA to determine the population of sunspots. They
take flux measurements between 3 and 14 GHz daily . Sunspot activity is cur-
rently of particular interest because recently the sunspot count has been lower than
models predicted . Monitoring changes in sunspot activity is an ideal task for
a small radio telescope operating in the GHz bands. It is also well-suited for the
detection of radio bursts, which are easy to identify because their intensity is many
orders of magnitude higher than that of the quiet Sun.
Like many other celestial bodies, the Sun appears larger at lower radio frequencies
than it does in the visible spectrum. This means that even for a low-resolution radio
telescope, the beamwidth is smaller than the size of the source, and it is possible to
measure features rather than just continuum emission. For example, even a small
radio telescope has the capability to determine if the upper hemisphere of the Sun
emits stronger than the lower hemisphere.
2.4.2 Neutral Hydrogen
In 1944, H. C. van de Hulst theorized the existence of a 1420 MHz spectral line
which was experimentally confirmed from observations of the Milky Way by Ewan
and Purcell in 1951 . Quantum mechanics predicts energy emission by atoms
in the radio frequencies by hyperfine splitting. This splitting arises from magnetic
dipole interactions between the nucleus and the electron. The hyperfine splitting
of hydrogen atoms in the ground state produces this 1420 MHz radiation. Given a
proton spin of s = 12
and an electronic angular momentum quantum number l = 12
it can be shown that the energy difference between the hyperfine energy levels in
26 Chapter 2. Theory
hydrogen is given in atomic units by
where µ is the reduced mass of the electron, gp = 5.5883 is the Lande factor of the
proton, and α is the fine structure constant. Complete derivationis of this energy
can be found in quantum mechanics texts such as ref . Using this relation the
frequency of the emitted energy can be calculated as 1420 MHz, which corresponds
to a wavelength of 21 cm. For a hydrogen atom this transition occurs with an average
frequency of 2.9 × 10−15 Hz. This may seem a rare occurrence, however due to the
abundance of hydrogen in the universe it is relatively common. The center of the
Milky Way as well as HII regions and the Sun are rich in neutral hydrogen.
2.4.3 The Milky Way
The view of the Milky Way galaxy from Earth is obscured by high amounts of dust
opaque at visible wavelengths but transparent at RF . As a result, radio tele-
scopes can probe deeper areas of the galaxy than optical telescopes. Similar to the
Sun, radio emission from the Milky Way is divided into three components: ther-
mal bremsstrahlung and spectral emission from HII plasmas, synchrotron radiation
emitted by supernova remnants, and spectral emission from an abundance of neutral
hydrogen (1.4 GHz) and hydroxyl (1.7 GHz) . Monitoring the radio emission of
the Milky Way is an effective way to measure the galactic rotation curve. A simple
model to predict the rotation of the galaxy is 
where M is the mass of the galaxy concentrated at the center, G is the gravitational
constant, and R is the distance from the central mass. From some arbitrary point on
2.5. Radiometer Design 27
the disc of the galaxy, we will observe the maximum angular velocity when it is in
the direction of our line of sight. As a result, the observed frequency of radiation will
be redshifted. This is especially useful when looking at spectral emission, since the
precise frequency of radiation with no redshift is known and can be compared to the
measured frequencies. When monitoring the neutral hydrogen emission of the galaxy
over time, it has been shown that the frequency of highest flux density varies by ± 5
MHz . Using these data we may determine how the galaxy rotates with respect
to the Solar System.
2.5 Radiometer Design
Radio astronomers are fortunate enough to work with signals of a sufficiently low
frequency such that they can be manipulated using electronics rather than optics.
The radio telescope collects radiation not using lenses and mirrors, but with circuitry.
The radio receiver is the most important part of the radio telescope and represents
the most significant design challenge. The most efficient methods for dealing with
high frequency radio signals using electronics are well understood, so most telescope
radiometers are similar in their functions. However, the methods for implementing
these functions vary widely.
2.5.1 Superheterodyne Model
The top-level organization of most radio telescope receivers follows a common design
format. A block diagram of a typical superheterodyne receiver can be seen in Fig
2.8. The RF signal from the antenna is amplified using a low noise amplifier (LNA)
which in some systems is cryogenically cooled to reduce noise. This amplified signal
is converted, or modulated, to a lower intermediate frequency (IF) by mixing the
28 Chapter 2. Theory
incoming RF signal with an artificial waveform supplied by a local oscillator. This
IF signal is filtered using a narrowband band-pass filter. A square law diode rectifier
converts the filtered IF signal to a voltage proportional to its power. The output
voltage can be sent to a waveform analyzer or converted to a digital signal using a
voltage-to-frequency converter and finally processed by a computer for data collection.
2.5.2 Frequency Mixing
Radio frequency signals are cumbersome to process so the superheterodyne receiver
employs a mixer to convert the RF signal to a lower IF. This allows modules to be
designed for one specific IF despite the wide bandwidth of RF signals received by the
antenna, which is desirable because signals incident on radio antennas are difficult
to amplify efficiently at their native frequencies . Signal processing, especially
using analog methods, is similarly diffcult. Converting the input to an IF simplifies
transmission as well, since high quality cable is needed to transmit RF signals with-
out significant power loss, especially over long distances. Frequency downconversion
solves all of these issues but not without introducing some design challenges.
A frequency mixer, or multiplier, outputs a superposition of signals consisting of
the sum and difference of the two input frequencies, each with a phase shift of 90
degrees relative to the input. In a radio telescope receiver, one of these signals is the
RF input signal (i.e. the raw signal measured by the telescope antenna) and the other
signal is an artificial waveform produced by a local oscillator. Local oscillator circuits
can be constructed using crystals, voltage-controlled oscillators (VCOs), or digital-
analog converters (DACs.) VCOs and DACs provide the advantage of tunability -
astronomers who wish to target a specific input frequency to examine, such as a
spectral emission line, would require the ability to tune their local oscillator with a
reasonable degree of precision. Using a DAC generally requires a microcontroller.
2.5. Radiometer Design 29
The behavior of a frequency multiplier is clearly illustrated by the trigonometric
sinA sinB =1
2[cos(A−B) − cos(A + B)] (2.36)
Only the lower, subtracted frequency component is desired - the summed component
is called the image. The image is a potential source of high frequency noise for the
IF section of the receiver. Isolating the RF image and the LO from the IF signal is
an important aspect of receiver design. Filters usually immediately follow frequency
mixers to eliminate the image signal.
2.5.3 Square Law Detection
A square law detector is in essence a half-wave diode rectifier with a low pass filter.
A simple half wave rectifier consists of a diode with a resistor to ground in parallel
with its input. For large signals, a capacitor placed in parallel with the output will
hold the output voltage near the peak voltage of the AC input. For smaller input
signals, the behavior is more complicated.
The current-voltage curve of a diode is described by the Schockley Diode Equation
I = IS(expVD
− 1) (2.37)
where IS is the reverse bias saturation current, VD is the voltage across the diode,
n is a unitless coefficient called the quality factor, and VT = kT/q is the thermal
voltage. Generally the behavior of diode detectors is separated into three regimes
governed by this current-voltage curve. For high VD (nominally +20 dBm and above)
the output voltage of a detector goes linearly with the input voltage, as described. At
less than +20 dBm, we approach the regime where VD ≈ VT and the proportionality
of the output to the input is hard to predict. Below a nominal -20 dBm, we enter
30 Chapter 2. Theory
the square law region. Small-signal analysis shows the behavior of the diode in this
regime. Consider a diode connected to a simple RC low-pass filter. Since the I-V
relationship of the diode is inherently exponential, we can expand it in a power series
iD = c1vD + c2v2D + c3v
Suppose that the small-signal input voltage is sinusoidal so vD = A cos(ωt). Then
applying the appropriate trigonometric identities, we have
iD = c1A cos(ωt) +c2A
2(1 + cos(2ωt))
c3A3(cos(3ωt) + 3 cos(ωt))
which simplifies to a constant proportional to A2 plus terms containing harmonics of
cos(ωt). The low-pass filter connected to the output of the diode will filter out these
sinusoidal terms, so they become negligible. In the context of small-signal analysis,
vout = iDRL, so the output of the square law detector is
V0 = αRLV2i (2.40)
where α is some constant. To express it in a way that is more applicable to radio
V0 ∝ Pi (2.41)
where Pi is the input power. Notice that this only describes how the output is
proportional to the input and so we cannot calculate the absolute input power from
the output. These calculations are made possible by telescope calibration.
2.6 Radiometer Calibration
The behavior of radiometer output is more commonly discussed as a temperature
rather than a voltage or power level. The so-called noise temperature is defined by
P = kBTsBn (2.42)
2.6. Radiometer Calibration 31
where P is the power delivered by a noise source, kB is Boltzmann’s constant, Ts is the
noise temperature and Bn is the bandwidth of the signal in Hz . The noise figure, a
common specification on RF electronic components, describes how the intrinsic noise
of the component degrades the quality of the signal being passed through it. It is
defined as the ratio of the signal-to-noise ratios in decibels, or 
F = 10 log(SNRin
The first step toward calibrating a radiometer is to determine its intrinsic noise tem-
perature which describes its noise output when no input is present. It would be
convenient if we could point the telescope at something which produces absolutely no
radio frequency radiation, however such things do not exist, so calibration becomes
a more complicated process. To do this we compare the behavior when the telescope
is pointed at sources of known flux density. Most often the Sun is used as a refer-
ence and is compared to the observed temperature of the ”cold sky”, or some region
of space that does not have a strong radio emitter. The noise temperature of the
antenna can be written as
2KB(Ssrc/Ssky − 1)− Tsky (2.44)
where Ssrc is the known flux density of a measured source and Tsky is the measured
temperature of a cold point in the sky. For example, if the Sun were to be used as a
calibration source, we would first calculate the ratio of the observed flux density of
the sun and the observed flux density of some quiet point in the sky.
32 Chapter 2. Theory
Figure 2.7 A plot of the radio frequency radiation from the Sun as a functionof wavelength. Frequency is given along the top in MHz. At Ku Band (10 to12 GHz) we can measure quiet Sun bremmstrahlung as well as synchrotronradiation arising from sunspots and intense radio bursts. Source: 
2.6. Radiometer Calibration 33
Radio Signal IF Signal DC Voltage
Figure 2.8 A functional block diagram of a typical superheterodyne receiver.A low noise amplifier amplifies the input signal before it is converted down toan intermediate frequency and filtered using band-pass filters. The filteredoutput is passed through a diode detector which converts the AC signal to aDC power level.
34 Chapter 2. Theory
Design and Implementation
The radio telescope described in this paper was designed to be flexible and inexpensive
without sacrificing too much radiometer sensitivity. Less than $700 was spent on the
project, almost all of which was spent on developing the receiver. The telescope can
only operate in drift mode at this time due to lack of automated motor control.
The telescope antenna is a 3m parabolic dish previously used to receive a satellite
internet connection, provided free of charge by a donor in Spencer, NY. The telescope
is planted outside the Clinton Ford Observatory at Ithaca College. We plan to mount
it such that it points toward the equator and both the Sun and the center of the Milky
Way will pass through the beamwidth. This is sufficient for simple flux measurements
of these accessible sources.
36 Chapter 3. Design and Implementation
The resolution of an ideal parabolic antenna can be modeled by 
R = 1.22λ
where D is the diameter of the dish and λ is the wavelength of radiation being ob-
served. A smaller value of R corresponds to a more narrow beamwidth. Objects with
smaller angular size in the sky can be resolved by telescopes with better resolutions.
At Ku band (λ ≈ 3 cm), then, the resolution of our 3 meter parabolic antenna is
about 0.01 rad or about 35 arcminutes. This is comparable to the apparent size of
The gain of a parabolic antenna is modeled by
where G is the d is the diameter of the dish, λ is the wavelength observed, and eA is
a term which describes the efficiency of the dish. Typically, parabolic antennas range
in efficiency values from 0.5 to 0.75 . Assuming that our dish is perfectly efficient,
we expect a gain of about 120 dB, but realistically the gain probably lies somewhere
near 80 dB. Calibration will determine a specific value.
3.2 Superheterodyne Receiver
The receiver developed for this project is an adaptation of the analog version of
Haystack Observatory’s Small Radio Telescope (SRT). A newer, digital version of the
SRT is also commercially available, and complete schematics for both versions as well
3.2. Superheterodyne Receiver 37
as some limited documentation are freely downloadable on the MIT website .
These schematics served as the basis for our circuit designs. The IF filters and
amplifiers used here remain largely unchanged, with only a few component values
changed to improve efficiency. The local oscillator and power supply circuits have been
redesigned to suit the desired functionality, and some extra amplifiers for enhanced
drive capability have been added. Since the SRT is designed to receive L Band signals
and we have engineered our telescope for Ku Band, we have purchased a Ku Band
Low Noise Block (LNB) which downconverts a Ku Band input signal to L Band.
The complete receiver receives a Ku Band input which is downconverted to L
Band at the feed horn, transmitted to an RF Receiver board also placed at the horn
which mixes the L band signal down to audio frequencies, and finally transmitted via
coaxial cable to a second circuit board which holds additional filter-amplifiers and a
square law detector. The output of this second board goes to a computer for data
collection. For complete schematics of the final design, images of the PCB layout,
and photographs of the circuit boards, see Figs 3.3 and 3.2. A block diagram of the
complete system can be seen in Fig 3.1.
3.2.1 Ku Band Low Noise Block
Lumped-element circuits, even with the smallest surface-mount components, are not
well-behaved at frequencies above 10 GHz. It is possible to construct such circuit
boards, however it requires the precise impedance control of microstrip board traces
to prevent signal loss due to reflections. This type of impedance control dramatically
increases the price of PCB fabrication to the point that it was not feasible for this
project. As a far more affordable alternative, we sought to purchase a commercial
Low Noise Blocks (LNBs), as they are referred to in the satellite communications
38 Chapter 3. Design and Implementation
100 MHz-DC 0°
Audio Audio DC
Figure 3.1 Block diagram of the complete telescope. The Ku Band (11GHz) input signal undergoes two frequency modulations and several stagesof amplification and filtering before being rectified to a DC voltage by thesquare law detector. The output of the square law detector is connected toa computer for data collection.
3.2. Superheterodyne Receiver 39
Figure 3.2 Schematic of the RF receiver circuit, which connects directly tothe output of the LNB. It houses the frequency mixers, local oscillator, andphase detecting filters.
40 Chapter 3. Design and Implementation
Figure 3.3 Schematic of the IF detector circuit, which houses the 4-poleButterworth filter and the square law detector.
3.2. Superheterodyne Receiver 41
industry, consist of a high gain amplifier, a frequency mixer for down-conversion, and
sometimes a phase-locked loop for stability control. They are designed to receive high
frequency signals from satellites at the antenna, usually at C band, Ku band, or more
rarely X band. It amplifies these signals and converts them to an IF suitable for
transmission along common coaxial lines. Thus, they serve the exact same purpose
as the first stages of a superheterodyne receiver.
LNBs can be found for a wide range of prices. Aside from designated frequency
input, they are specified for gain, overall noise figure, phase noise, voltage stand-
ing wave ratio, and local oscillator stability. The most inexpensive LNBs are noisy
and have typical voltage standing-wave ratios (VSWR) of 3:1 or worse. VSWR is a
specification that describes how much power is typically lost due to the reflections
of electromagnetic waves propogating through the device. Perfectly designed devices
have uniform impedance throughout and produce no reflections, so the VSWR is 1:1.
Inexpensive LNBs also allow for drifting of the local oscillator frequency by 1 MHz
or higher. These devices are sufficient for a satellite TV receiver, which receives high
amplitude signals and does not pass them through much further amplification before
they reach their destination. However, for a radio telescope, too much intrinsic noise
at the antenna can render the entire system unusable. The smallest noise signal will
be amplified by each successive amplifier stage in the receiver and can become large
enough to obscure telescope measurements. As a result we chose to purchase a high
quality industrial-grade LNB with lower noise figures. The LNB was purchased from
Orbital Research (model LNB1075S-500P-WF65) for $280. It specifies a noise figure
of 0.6 dB with a gain of 65 dB.
Generally, LNBs do not have a separate connector port for a power supply. It is
expected that the power supply voltage will be multiplexed with its output signal as
shown in Fig 3.4. In typical communications applications this is accomplished with a
42 Chapter 3. Design and Implementation
10 MHz Ref
DC In To Modem
DC PowerRF Only
Figure 3.4 A multiplexer is the conventional method of supplying power toan LNB. A DC power signal is connected to the multiplexer which passespower to the LNB and receives the RF signal from the LNB through thesame port. The multiplexer passes this RF signal to the modem (the receivercircuit board) but blocks the DC power through this port. As a result thereceiver must be powered by other means.
multiplexer, called a bias tee, which is built in to commercial satellite modems. The
manufacturers of the LNB were kind enough to provide me with a bias tee, usually
priced at $100, free of charge. For inputs the bias tee takes the LNB power supply
and its output signal. It also has a port for a 10 MHz reference signal for external
local oscillator control, but our LNB does not have this feature. The bias tee allows
the power supply signal to flow into the input of the LNB but blocks it from flowing
through its output, which goes to the rest of the receiver.
3.2.2 L Band Frequency Mixer and Local Oscillator
As part of the telescope receiver, the LNB amplifies the raw Ku band signal by a
nominal 65 dB and downconverts it to L band. This L band signal is a suitable input
for the printed circuit boards we have developed. The local oscillator signal on this
board is generated by a voltage controlled oscillator (VCO), Minicircuits JTOS-1550.
This chip was chosen because the control pin can rest at its minimum voltage and
a suitable signal will still be produced. It has a frequency output of between 1150
and 1550 MHz depending on the control voltage, ranging from 0.5 V to 20 V. A
3.2. Superheterodyne Receiver 43
potentiometer has been placed on the tuning pin so that the LO frequency can be
tuned if desired. The LO signal emitted by the VCO is amplified by a nominal 6
dBm using a monolithic amplifier before being passed to a passive 90 power splitter,
Minicircuits QCN-19D. This splitter outputs two signals, one in phase with the LO
and one 90 out of phase. The splitter provides no amplification so the outputs are
each at roughly half the power level of the input.
The L band signal transmitted from the output of the LNB is independently mixed
with these two signals using a a pair of Minicircuits RMS-11F+ frequency multipliers.
The purpose of splitting the RF signal in this way is so that they can be filtered using
phase detector circuits, which provide a high level of isolation from the unwanted
3.2.3 Filter-Amplifier Stages
The purpose of the circuits following the RMS-11F+ frequency mixers are to greatly
amplify the signal and filter it to a pass-band with corner points at 10 KHz and 70
KHz. The outputs of the frequency mixers are first passed to identical non-inverting
amplifiers constructed using high speed op-amps, Analog Devices 797ARZ. These op-
amps produce a gain of 20 dB. Following both of these amplifiers are all-pass filters,
also called a phase detector. The all-pass filter, as its name suggests, passes signals
of all frequencies (within the limits of the op-amp) with unity gain, and changes only
the phase of the output. The phase shift produced by the all-pass filter can be written
in radians as
ϕ = π − 2 arctan(ωRC) (3.3)
The capacitance values in our circuit are 10 nF for the in-phase signal and 1500 pF for
the out of phase signal. The resistance values are the same for both - 1K. The outputs
of these all-pass filters are combined into one signal - when they are in phase, the
44 Chapter 3. Design and Implementation
maximum amplitude will be produced. When they are out of phase, the total signal
will be greatly attenuated. From this, we can see how the phase detector filters out
unwanted frequencies. At 40 KHz, the center of the passband, the in-phase signal is
shifted by 138 while the quadrature-phase signal, already 90 out of phase, is shifted
by an additional 43 for a total phase shift of 133. The result is a superposition
of signals which are only 5 out of phase. As the input frequency moves away from
the center passband, the output signals becomes further out of phase until reaching a
90 phase shift at DC and total deconstructive interference (180 phase shift) at high
frequencies. Testing these circuits using artificial sine wave inputs produced good
results, yielding unity gain at all tested frequencies for the individual phase detectors
and a maximum amplitude mixed output near 40 KHz as seen in Fig 3.5.
The blocked frequencies were found to decrease by roughly 15 to 20 dB per decade
but attenuated to zero quickly.
Two more unity gain filter-amplifiers reside on the IF circuit board. Together
these make a 4-pole Butterworth filter. This filter is designed to improve the flatness
of the passband between 10 KHz and 70 KHz. A common way to describe a filter is
by its transfer function. The transfer function, denoted H(s), is defined as the ratio
of the laplace transform of the output voltage to the laplace transform of the input
H(s) =Y (s)
The laplace transform converts a function in the time domain to one in the frequency
domain, thus, the transfer function is a time-independent expression for the filter’s
complex gain as a function of frequency . The transfer function of this topology
is given in general as 
Z1Z2 + Z4(Z1 + Z2) + Z3Z4
3.2. Superheterodyne Receiver 45
20 30 40 50 60 70 80 900.15
Figure 3.5 Plot of the gain of the image rejection mixer built from two all-pass filters with different input reactances. The pass band is observed to benear 40 KHz as anticipated.
46 Chapter 3. Design and Implementation
Figure 3.6 The band pass filter used in the audio section of our super-heterodyne receiver consists of two Sallen-Key filters in series, which havethe topology pictured above. (Source: Wikimedia Commons)
where the impedances Z are specified according to the diagram in Fig 3.6. Specifically,
this Butterworth filter is two Sallen-Key filters placed in series. The Sallen-Key
topology has a cutoff frequency at 
so these filters have a frequency cutoff at roughly 25 KHz (Q300 in Fig 3.10) and
60 KHz (Q301). Gain is approximately equal to +53 dB within this pass band, and
decreases at a nominal 80dB per decade outside of the pass band. Bench tests with
this circuit confirm the passband suggested by the theory as shown in Fig 3.7.
3.2.4 Detector Circuit
The receiver has two outputs, one on the output of a square law diode rectifier and
another right before the input to the detector. The AC output can be used to trou-
bleshoot the detector, and is also useful if one wants to bypass the square law detector
3.2. Superheterodyne Receiver 47
20 30 40 50 60 70
Figure 3.7 A plot of the measured gain of the 4-pole Butterworth filter onthe IF circuit board. The experimental gain is depicted in blue, and a plotconstructed from an LTSpice simulation is depicted in red. This filter consistsof two Sallen-Key filters placed in series, with the first (Q300) providing low-pass filtering and the second (Q301) providing high-pass filtering. Thesefilters are designed to provide a pass band between 25 KHz and 60 KHz.
48 Chapter 3. Design and Implementation
entirely. Converting the AC signal to a DC voltage is done in hardware with the square
law detector but it is equally viable to do it using software.
The square law detector is designed using a germanium schottky diode. Schottky
diodes have a nominal forward voltage of 0.2 V . A resistor network connected to
the power supply biases the anode and cathode of the schottky diode such that when
the input amplitude is zero, the diode rests near the edge of saturation. A 0.1 uF
capacitor rectifies the output signal into a DC voltage. Since this signal is weak, an
amplifier has been inserted on the output. This amplifier is a non-inverting op-amp
based amplifier with a nominal voltage gain of 50.
3.2.5 Printed Circuit Board Design
Our receiver is split into two circuit boards, one which houses the radio frequency
components and initial amplifiers, and another which completes the filtering and
houses the diode detector. This was done so that the RF circuits would be small
enough to fit in the feed horn of the antenna with the LNB. Transmitting the L band
signal from the LNB over any long distance could cause power loss due to reflections.
Additionally, the RF circuits are such that small-scale surface mount components
must be used to prevent radiative power loss. In the IF board the signals are on the
order of 50 KHz so this is not a concern.
The free CAD software suite ExpressPCB was used to draw the schematics and
PCBs for the receiver. The PCB drawings for the RF and IF boards can be seen in
Fig 3.9 and 3.10 respectively.
SMT soldering is done using a process called reflow soldering, where instead of
using a traditional soldering iron to heat connections, the board is placed in a reflow
oven and heated using a specified heat profile. Solder paste is used to secure compo-
nents to their pads before heating. When the paste reaches temperatures above 200
3.2. Superheterodyne Receiver 49
50Preheat Soaking Reflow
60 120 180 240
Time (s)Time (s)
Figure 3.8 A plot of the suggested heat profile for successful reflow solderingusing 64Sn/36Pb solder paste. This heat profile was used to solder SMTcomponents to our PCBs using a common commercial frying pan.
C the metals inside melt and the connection is made. The solder paste used here is
64% tin and 36% lead. It is specified as a free-flowing solder paste, which is more
diluted than a solder paste specified for restricted flow. Free-flowing solder paste is
hard to work with when making very small connections. For example, one would not
choose a free-flowing paste to solder a 64-pin microcontroller. For our purposes it
proved easy to work with. Lacking a true reflow oven, we opted to use a frying pan
instead. In an informal study by Sparkfun of inexpensive SMT soldering methods
this was shown to be the best. The heating profile used for soldering is depicted in
50 Chapter 3. Design and Implementation
Figure 3.9 PCB layout schematic of the RF receiver circuit which receivesthe signal from the LNB at the antenna. Our PCBs were designed usingExpressPCB software. Most components are surface-mounted and were sol-dered by reflow soldering. The green represents the ground plane on thebottom of the board while the red represents traces and plane connectionson the top of the board. The silkscreen is in yellow.
3.2. Superheterodyne Receiver 51
Figure 3.10 PCB layout schematic of the IF detector circuit which is po-sitioned on the ground near the computer used for data collection. Mostcomponents here are through-hole and were soldered by hand. The colorscheme is the same as in the RF board.
52 Chapter 3. Design and Implementation
Results and Testing
4.1 Data Collection
Collection of raw radio telescope data is done using Matlab software. The receiver
output signal is connected to a NIDAQ DaqCard 6024E interface. This interface is
connected to a laptop PC through PCMCIA which runs the Matlab script. It has a
maximum sample rate of 200 KHz and 12 bits of resolution. At the maximum voltage
input range of 10 V this corresponds to a resolution of 2.4 mV. The MATLAB script
monitors the voltage at the DaqCard port at the given sample rate and stores it in a
vector with a timestamp. This is more than sufficient for the expected outputs. The
code for this software can be found in Appendix A.
4.2 Receiver Testing
Rigorous bench testing of the complete telescope receiver requires a suitable test
input signal. The ideal input signal for testing is a Ku band noise source, however
any RF signal generator operating near Ku band would suffice. Commercial RF
54 Chapter 4. Results and Testing
generators and noise sources are expensive and were not available for this project, so
an alternative method of testing was necessary. A 10.5 GHz microwave transmitter
and an RF frequency meter were obtained for this purpose. We have also obtained
a commercial frequency meter that is capable of measuring signals up to 3 GHz in
frequency. This allows us to characterize the signals flowing through the L band
portion of our circuitry.
The 10.5 GHz signal from the microwave horn lies outside the specified bandwidth
of the LNB, and so we expect the filters in the LNB to attenuate the signal. Also
note that the majority of the power from this signal will not pass through the filter-
amplifiers since its frequency is too high. For this reason, power measurements are
not especially useful, however we may still draw conclusions about the behavior of
the receiver by examining the output. The frequency meter reports a signal at the
output of the LNB centered near 850 MHz, which is in agreement with the expected
intermediate frequency specified in the LNB datasheet. We also observe this signal
at the input to the RMS-11F frequency mixers. The output of the mixers produces
a signal which appears to be centered near 200 MHz. Given that the local oscillator
operates at about 1100 MHz, 200 MHz is approximately the difference of the two
inputs, so this is a reasonable result. From this we conclude that the receiver is
correctly mixing the L band input and the local oscillator signals.
At the audio output of the receiver we observe the filtered signal via PCMCIA
interface as recorded by the Matlab software. Manually waving the microwave horn
across the beam of the LNB produces a noise-like signal that is much stronger than the
receiver’s background noise. Around the edges of the beam, the measured intensity
is decreased because only part of the microwave signal emitted from the horn is
absorbed. When the horn is placed directly perpendicular to the LNB, the maximum
amplitude is produced. We have chosen to check this signal at the audio output
4.2. Receiver Testing 55
3 3.5 4 4.5−500
Figure 4.1 Demonstration of the receiver collecting Ku band radio wavesand converting them to an amplified audio frequency signal. This outputis the result of passing 15 mW of microwave radiation at 10.5 GHz directlyin front of the beam of the LNB and recording the output via PCMCIAinterface. At the maximum amplitude of the output we see a voltage of 420mV corresponding to a 50 Ω-matched power of 3.6 mW. Notice that despitethe large amounts of gain in the receiver, the output is lower in power thanthe original input signal - this is due to the fact that the input frequency liesoutside the pass band of the LNB.
56 Chapter 4. Results and Testing
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2−8
Figure 4.2 With no power supplied to the LNB the intrinsic noise of thereceiver is observed to be on the order of 2 to 4 mV, corresponding to less than1 µW of RMS power. The resolution limitations of our computer interfaceis evident. While this does not reveal the noise temperature of the overallsystem since the noise of the LNB is not taken into account, it does showthat the filter-amplifiers generate very little noise, as expected.
rather than at the output of the square law detector because the signal is strong, and
lies outside of the square law region of the diode, which is near -20 dBm. This shows
that even with the frequency band mismatch, a 15 mW signal incident on the LNB
antenna is enough to drive the detector well beyond its intended input range, which
results in non-linearity. Astronomical signals will be significantly weaker and we do
not expect to have this problem when taking real measurements.
Conclusions and Future Work
We have successfully developed an antenna and receiver system which collects and
measures Ku band radio waves. Based on laboratory testing we find that the receiver
is sufficiently sensitive such that the telescope will be capable of detecting astronom-
ical sources of radio such as the Sun and the Milky Way. Due to time constraints,
astronomical data has not yet been collected with the telescope at the time of this
writing. A mechanism for the mounting of the antenna is currently in development.
We expect to begin calibrating the telescope and conducting simple measurements
when the antenna has been successfully mounted.
5.1 First Expected Observations
The antenna mount will allow us to steer the beam of the telescope and aim it at
specific sources of radio. Since the Sun is low in the sky in the winter months this will
be necessary for solar measurements. Once the telescope is mounted and the receiver
is properly set up for data collection at Ford Observatory, we will be able to calibrate
the system using the process described in Section 2.6. This process should include a
58 Chapter 5. Conclusions and Future Work
measurement of the total flux from the Sun, since that is the most accessible radio
source in the sky. This can be compared against the flux measured by professional
solar observatory such as SOHO. For a hot reference source, the simplest method
would be to point the dish at the observatory building or at the ground if possible.
If the calibration of the telescope and measurements of the Sun are successful, the
next target for measurement should be the Milky Way. Positioning of the telescope
beam is not crucial in this case since the galaxy covers a large portion of the night
sky and it is likely that some part of it would pass through the beam at some point
in the day. A common method of calibrating smaller radio telescopes is to cool a slab
of foam to liquid nitrogen temperatures and point the beam toward it.
5.2 Longterm Goals
If it is found that the telescope receiver is sensitive enough to observe more elusive
sources of radio or distinguish between the Sun’s levels of radio activity due to radio
bursts, as we expect it may be, an automated and computerized steering system will
have to be developed. This constitutes a significant longterm mechanical engineering
project and may also be expensive. Little research has been done on steering mecha-
nism designs thus far since we have mainly been concerned with the viability of drift
Given a computerized steering mechanism, we would be able to conduct some sim-
ple research tasks with the telescope. This includes monitoring the Sun for increased
sunspot activity which manifests itself as a stronger flux in the radio range. The most
effective way to monitor for these changes is to program the telescope to follow the
Sun across the sky and record the data over several days (or weeks.) We may also
measure the galactic rotation curve of the Milky Way by similar tracking methods.
5.2. Longterm Goals 59
The possibility of observing at L band can also be explored. The primary moti-
vation for observing at L band is to measure emission from neutral Hydrogen. Most
smaller radio telescopes operate in this band, so the expected results are also well-
documented. Converting the receiver from Ku band to L band can be accomplished
simply by replacing the Ku band LNB with a low noise, high gain amplifier since the
second stage of the receiver is designed to receive L band signals. However, since our
LNB also acts as the feed, a custom feed horn would have to be developed.
60 Chapter 5. Conclusions and Future Work
Below is the Matlab script used to collect data from the output of the receiver. It
has been adapted from a script written by Dr. Bruce Thompson for PHYS 360,
Intermediate Physics Laboratory, at Ithaca College.
function[data,t]=GetAnalogData(deviceName, NofChannels, SampleRate, NofSamples);
\% function to get analog data via the National Instruments DAQ card
\% NofChannels - the number of channels to aquire, sampling will be
\% sequential from channel 0 to N-1
\% SampleRate - the sample rate in Hz
\% NofSamples - total number of samples to obtain per channel
\% data - data samples in NofChannels columns
\% t - times of the samples in data
\% set up analog IO
62 Appendix A. Matlab Script
daq = daqhwinfo(’nidaq’)
device = deviceName;
daq = daqhwinfo(ai)
set(ai, ’SampleRate’, SampleRate);
\%initiate the device
\% show parameters and wait for start keypress
sprintf(’NChan: \%2i SRate: \%f NSamples: \%6i Time: \%f\n’, ...
NofChannels, SampleRate, NofSamples, TT);
\% Clear the memory upon completion
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