Amplitude Modulation Early Radio EE 442 Spring 2017 · AM Modulation -- Radio 5 Amplitude...
Transcript of Amplitude Modulation Early Radio EE 442 Spring 2017 · AM Modulation -- Radio 5 Amplitude...
AM Modulation -- Radio 1
Amplitude Modulation – Early Radio EE 442 – Spring 2017
D. B. Estreich
http://www.technologyuk.net/telecommunications/telecom_principles/amplitude_modulation.shtml
LO audio baseband mf f f
AM Modulation -- Radio 2
Modulation Options
AM Modulation -- Radio 3
Amplitude Modulation Illustrated
Radio Carrier fC
Audio tone fm
Amplitude Modulated
Signal
fC >> fm
AM Modulation -- Radio 4
Baseband versus Carrier-Based Communication
Baseband communication is the transmission of a message as generated.
Carrier communication requires the modulation of a message onto a carrier signal to transmit it over a different frequency band. We will use modulators or mixers to do the frequency translation.
(Note: “Pulse modulated” signals, such as PAM, PWM, PPM, PCM and DM are actually baseband digital signal coding (and not the result of frequency conversion).
Use of Sinusoidal Carriers: With a sine waveform there are 3 parameter s which we can “modulate” to carry a message on a carrier – they are the amplitude, frequency and phase of the sinusoid.
AM Modulation -- Radio 5
Amplitude modulation (AM) is a modulation technique in which the amplitude of a high frequency sinusoidal carrier (a radio frequency carrier at frequency fC) is varied in direct proportion to a modulating baseband signal, m(t). The modulating signal contains the intended message, data or information – sometimes consisting of audio, as in radio broadcasting, or two-way radio communications as in cell phone conversations.
The high frequency carrier is modulated by combining it with the modulating signal, m(t), using a multiplier or mixer.
Amplitude Modulation (Verbal) Definition
AM Modulation -- Radio 6
Amplitude Modulation in Pictures
100 kHz carrier modulated by a 5kHz audio tone
100 kHz carrier modulated by an audio signal
(frequencies up to 4 kHz)
5 kHz Audio tone
Tone modulated AM signal
Baseband Voice modulated AM signal
Frequency Domain Time Domain
AM Modulation -- Radio 7
Example: Voice Signal – 300 Hz to 3400 Hz Baseband
time
amp
litu
de
m(t)
Symbol m(t) represents the source (baseband) message signal.
Time Domain
AM Modulation -- Radio 8
Frequency Domain
Voice Band for Telephone Communication
Voice Channel 0 Hz – 4 kHz
Voice Bandwidth 300 Hz – 3.4 kHz
f 0 Hz 300 Hz 3.4 kHz 4 kHz 7 kHz
PSTN
AM Modulation -- Radio 9
3,400 Hz
Speech signal
Speech spectra
Representative Voice Spectrum for Human Speech
For the telephone AT&T determined many years ago that speech could be easily recognized when the lowest frequencies and frequencies above 3.4 kilohertz were cutoff.
Waveform as received from a microphone converting acoustic energy into electrical energy.
Fast Fourier transform of the above speech waveform showing energy over frequency from 0 Hz to 10 kHz.
AM Modulation -- Radio 10
A crystal radio receiver, also called a crystal set or cat's whisker receiver, is a very simple radio receiver, popular in the early days of radio. It needs no other power source but that received solely from the power of radio waves received by a wire antenna. It gets its name from its most important component, known as a crystal detector, originally made from a piece of crystalline mineral such as galena. This component is now called a diode.
Early AM Crystal Radio Receiver (The Bare Minimum)
Note: 1N34A is a germanium diode
Earphones
LC Tuned Circuit Selects Signal
Demodulator
Electrical to Acoustic
Transducer
C
11 AM Modulation -- Radio
Foxhole Radio (from World war I)
http://bizarrelabs.com/foxhole.htm
Ground
Coil – 120 turns of wire
Cold water pipe
Safety pin Razor blade
Earphones
“Earth” = Ground
Needle point
Demodulator
AM Modulation -- Radio 12
Diagram from 1922 showing the circuit of a crystal radio. This common circuit did not use a tuning capacitor, but used the capacitance of the coil and the antenna to form a “tuned circuit” with the coil.
Galena (lead sulfide) was probably the most common crystal used in cat's whisker detectors.
Crystal Radio Receiver from 1922
Sliding contact
AM Modulation -- Radio 13
AM Radio Kits in the 1950’s
http://onetuberadio.com/2015/01/06/1956-boys-life-conelrad-receiver/
AM Modulation -- Radio 14
AM Radio in the 21st Century
Parameter Value or Range
AM Broadcast Band 535 kHz to 1700 kHz
Channel Bandwidth 10 kHz
Channel Spacing 10 kHz
Carrier Stability 20 Hz about carrier fC
Maximum Broadcast Power 50 kW
Number of USA AM Stations 4,728 AM stations
AM Modulation -- Radio 15
Double-Sideband AM Modulation
( )m t
( )m t
( )m t
( )M f
( )M f
t
f
BB
2B
t fCfCf
LSBLSB
USBUSB
( )cos(2 )Cm t f t
( )cos(2 )Cm t f t( )m t
cos(2 )
CarrierCf t
Lathi & Ding; Page 181
Modulator
Frequency-shifting property
Double-sideband
(modulating signal) (modulated signal)
1
( )cos(2 ) ( ) ( )2
C C Cm t f t M f f M f f
AM Modulation -- Radio 16
Double-Sideband AM Demodulation
2
12
1 12 4
Output of mixer is ( ) ( ) cos(2 )
( ) ( ) 1 cos(2 2 ) , taking FT gives
( ) ( ) ( 2 ) ( 2 )
C
C
C C
y t m t f t
y t m t f t
F y t M f M f f M f f
Square-law mixer
( )cos(2 )Cm t f t
cos(2 )Cf t
Carrier
Demodulator
( )y t
2 Cf2 Cf f
12 ( )m t
Spectrum of y(t) LP Filter
Lathi & Ding; pp. 181-182
Note: No carrier is present
M(f)
AM Modulation -- Radio 17
Degree of Modulation: Modulation Index
The amplitude modulation “modulation index” is a measure of the extent of amplitude
variation upon the carrier. The AM modulation index measures the amount by which the
modulated carrier’s amplitude varies relative to its un-modulated amplitude level.
When expressed as a percentage is the same as the “depth of modulation.” It can be
expressed as:
where A is the carrier signal’s amplitude, and
M is the modulation amplitude (peak change in the RF amplitude relative
to its un-modulated value).
Example: For an AM modulation index of 0.5, the modulation causes the signal to increase
by a factor of 0.5 and decrease to 0.5 of the un-modulated carriers signal’s level.
( ) ( ) cos(2 )Cy t A m t f t
Modulation IndexM
A
AM Modulation -- Radio 18
AM Modulation Index Basics - Examples
50% Modulation
100% Modulation
150% Modulation
AM Modulation -- Radio 19
Single-Tone DSB Modulation & Demodulation
( )M f
f
f
f
Single tone modulation is cos(2fmt)
mfmf
Modulating signal’s spectrum
C mf fC mf f( )C mf f ( )C mf f
2 Cf2 Cfmf mf
DSB Spectrum
Demodulated signal spectrum
12 ( )M f
USBUSB LSBLSB
Lathi & Ding; Page 183
Suppressed by low-pass filtering
12
( ) cos 2 2 cos 2 2C m C my t f f t f f t
AM Modulation -- Radio 20
Sideband and Carrier Power
In general an AM signal takes the form of
( ) cos( ) ( ) cos( )AM C Ct A t m t t
Carrier Sidebands
The carrier power PC is the mean-square value of Acos(ct), which is [A2/2]. The sideband power PS is the power contained in m(t)cos (ct).
2
21( )
2 2C S
AP and P m t
The power efficiency is defined to be
2
2 2
useful power ( )100%
total power ( )S
C S
P m t
P P A m t
2
2Single tone: ( ) cos ; ( )2
C
Am t A t m t
modulation index
AM Modulation -- Radio 21
Power in AM Signals in General
0
0
1 2 22 2
0
2 2
( ) ( ) cos( ) cos( ) ( )cos( )
Carrier power is
1cos ( )
2 2
1Signal power is , whereas the
2message power uses an "appropriate" interval,
1( ) ( )
C
AM C C C
C C
C
S m
t T
m
t
t A m t t A t m t t
AP A t dt
P P
P m t m t dtT
AM Modulation -- Radio 22
Categories of Amplitude Modulation
Baseband spectrum Conventional or Full AM Double-Sideband-Suppressed Carrier (DSB-SC) Single-Sideband /Upper Sideband SSB/USB Single-Sideband /Lower Sideband SSB/LSB
f
f
f
f
f
AM Modulation -- Radio 23
Frequency Translation In General – from fC to fI
Multiplying a modulated signal by a sinusoidal moves the frequency band to sum and difference frequencies.
Note: Super-heterodyning: c + I ; Sub-heterodyning: c - I
Example 4.2: We want to convert from frequency C to frequency I .
Figure 4.7 Example 4.2
Lathi & Ding; Page 189
( )g t( ) cos( )cm t t ( ) cos( )Im t t
2 cos ( )c I t
2 f
Input frequency c Output frequency I
AM Modulation -- Radio 24
Modulators (or Mixers) – Types of Modulators
1. Electronic multiplier modulators
2. Nonlinear component modulators
3. Switching modulators
Integrated circuits have made it easy to buy inexpensive multipliers operating to very high frequencies with power gain.
Almost any nonlinearity will work, but a very inexpensive but strongly nonlinear device is a diode. Transistors are also nonlinear and work well as modulators.
Switching is an easily attained function with diodes and transistors in electronic circuits – especially in integrated circuits..
AM Modulation -- Radio 25
Multipliers Used for Modulation
difference frequency
1
2
Let signals ( ) and ( ) be RF & LO sinusoidal inputs.
If ( ) cos( ) and ( ) cos( ), then
( ) ( ) ( ) cos( ) cos( )
( ) cos(( ) ) cos(( ) )
RF LO
RF RF LO LO LO
RF LO RF RF LO LO
RF LO RF LO RF LO
g t s t
g t A t s t B t
y t g t s t A t B t
y t A B t t
sum frequency
RF
IF Multiplier
LO ( ) ( ) ( )RF LOy t g t s t
( )RFg t
( )LOs t
AM Modulation -- Radio 26
Using Nonlinearity For Modulation
Vo = Vdc + G Vi + A Vi2 + B Vi
3 + • • •
fRF = 0.8 fLO = 1.0
LO
RF
LO - RF LO + RF
Y(f)
f
2LO
- R
F
3RF 3LO
2LO
+ R
F
2RF 2LO
1 2 3 0
2RF
– L
O
2RF
+ L
O
Device Vi Vo
Let Vi = ARF
cos RF
t + BLO
cos LO
t , then we get frequencies,
Vi RF
and LO
(linear)
Vi2 (
RF +
LO), (
RF -
LO), 2
RF & 2
LO (square law)
Vi3 (2
RF+
LO), (2
RF-
LO), (2
LO+
RF), (2
LO-
RF), 3
RF & 3
LO
. . . through third order . . .
Conclusion: Nonlinearity generates new frequencies.
AM Modulation -- Radio 27
A “hopelessly unsophisticated” mixer.
Tom Lee (Stanford University)
The unbalanced single-diode mixer his no isolation and no conversion gain.
Single-diode mixers have been used in many applications --
(1) Detectors for radar in WW II (2) Early UHF Television tuners (3) Early radio receiver detectors (4) mm-wave & sub-mm-wave
receivers
IF
RF + LO
Using Nonlinearity For Modulation and Demodulation
Filter
A diode will work.
AM Modulation -- Radio 28
Demodulation: Nonlinear Component Demodulator
Lathi & Ding Figure 4.10
Page 196
1 13 5
At rectified output, the AM signal is multiplied by ( ), thus the half-wave
rectified ( ) is
( ) ( ( ))cos( ) ( )
1 2( ( ))cos( ) (cos( ) (cos(3 ) (cos(5 ) ....
2
C
C C C C
rectified
rectified
w t
V t
V t A m t t w t
A m t t t t t
dc term Baseb
.
and
1( )A m t other termsX
DC shift (eliminates A term)
LPF
FT of pulse train
AM Modulation -- Radio 29
Demodulation: AM Envelope Detector Circuit
Two conditions must be met for an envelope
detector to work:
(1) Narrowband [meaning fc >> bandwidth of m(t)] (2) A + m(t) 0
Lathi & Ding; Page 197
“Envelope Detector”
AM Modulation -- Radio 30
Choosing the RC Time Constant for an Envelope Detector
Time constant RC is too short. t
t Time constant RC is too long.
1
Design criteria is 2 2 CB fRC
AM Modulation -- Radio 31
Generating m(t)cos(2fct) using Convolution
Fold, Shift & Multiply
f
f
From Convolution Theorem: (t)m(t) Cn( f ) M( f )
F
F
M( f )
Cn( f ) (t)
m(t)
Output Spectrum
LO
RF
( )cos(2 )Cm t f t
AM Modulation -- Radio 32
Switching Modulator – Generating m(t)cos(2fct)
Figure 4.4 from Lathi & Ding;
Page 186 Pulse train
AM Modulation -- Radio 33
Example: Diode Ring (Switching) Modulator
Figure 4.6 from Lathi & Ding;
Page 188
1 1
3 5
4cos(2 ) cos(3 2 cos(5 2C C Cf t f t f t
cos(2 )CA f t
( )cos(2 )CK m t f t( )m tiv
Diodes are switched on and off
Output: DSB-SC
Diodes are matched
AM Modulation -- Radio 34
Analysis of the Diode Ring Modulator
The diodes are driven hard so they switch abruptly between ON and OFF states. Diodes D1 and D2 and ON while diodes D3 and D4 are OFF, an vice versa. The diode action is equivalent to generating a square wave w(t) with period T0. We accomplish this by driving the diodes with a frequency of fC = 1/T0.
1 1
3 5
4( ) cos( ) cos(3 ) cos(5 )C C Cw t t t t
Multiplying the modulating signal m(t) with w(t) results in
1 1
3 5
4( ) ( ) ( )cos( ) ( )cos(3 ) ( )cos(5 )C C Cm t w t m t t m t t m t t
After BPF this is the term giving AM modulated signal
AM Modulation -- Radio 35
Assumption: Diodes act a perfect switches (switch states: On or Off) and are controlled by the RF carrier signal (also called local oscillator).
Circuit Diagram of Diode Ring Modulator
T1 T2
D1
D2
D3
D4
RF carrier signal
cos(ct)
m(t) DSB-SC:
( ) cos( )Cm t tModulating Signal
Output:
Redraw the ring modulator:
http://electronicspost.com/ring-modulator-for-the-double-sideband-suppressed-carrier-generation/
AM Modulation -- Radio 36
DRM Operation on the Positive Half-Cycle of Carrier
T1 T2
D1
D2
m(t) = 0
cos(ct)
+
currents
These currents cancel in the
primary.
Diodes D3 & D4 are Off
Positive Half-Cycle:
Result: Diodes D1 and D2 are switched to conducting state.
AM Modulation -- Radio 37
DRM Operation on the Negative Half-Cycle of Carrier
T1 T2
D3
D4
m(t) = 0
cos(ct)
+
currents
These currents cancel in the
primary.
Diodes D1 & D2 are Off
Negative Half-Cycle:
Result: Diodes D3 and D4 are switched to conducting state.
AM Modulation -- Radio 38
DRM Operation With Modulating Signal Applied
With diodes D1 and D2 on, signal on secondary of T1 is applied to T2. Non-inverting output is the result.
T1 T2
D1
D2
+ _
+ _
+ _
+ _
+ _
+ cos(ct)
m(t)
+ _
+ m(t)
output
During the Positive Half-Cycle:
AM Modulation -- Radio 39
DRM Operation With Modulating Signal Applied
T1 T2
D3
D4
+ _
+ _
+ _
+ _
+ _
+ cos(ct)
m(t)
+ _
- m(t) output
With diodes D3 and D4 on, signal on secondary of T1 is applied to T2. Inverting output is the result.
During the Negative Half-Cycle:
AM Modulation -- Radio 40
Net Output of Transformer T2 is AM Signal
Output as it would most likely appear after BPF
t
1 2&D D on3 4&D D on
DSB-SC signal at primary of T2
m(t)
OUTPUT
LO rectangular waveform
t
Output is proportional to m(t) during the positive cycle, and proportional to –m(t) during the negative cycle.
Summary
http://electronicspost.com/ring-modulator-for-the-double-sideband-suppressed-carrier-generation/
AM Modulation -- Radio 41
Double-Balanced Diode Ring Mixer
LO input RF Input
IF Output
All internal processing is a balanced circuit which gives improved isolation.
Wire-wound toroid
transformer
AM Modulation -- Radio 42
Commercial Diode Ring Mixer (Mini-Circuits)
Mixer in surface- mount package
Ring of FET devices operated as nonlinear
resistances
AM Modulation -- Radio 43
Demodulator: Gilbert Cell Double-Balanced Mixer
IF Output
RF Input
LO Input
Widely used in microwave bands.
m(t)
AM Modulation -- Radio 44
Demodulation of DSB-SC Signals
Demodulation of a DSB-SC signal involves multiplication with the carrier signal – it is identical to modulation. Reference: Figure 4.1 in Lathi & Ding.
At the receiver, the incoming signal is multiplied by a local carrier of frequency and phase in synchronism with the incoming signal. The only difference between the modulator and demodulator lies in input signal and the output filter.
With an incoming signal with suppressed carrier , the receiver must generate a local carrier which is synchronous in phase with the incoming signal. These demodulators are called synchronous or coherent demodulators.
Example 4.3 in Lathi & Ding;
page 190.
AM Modulation -- Radio 45
Spectrum of Conventional AM (DSB with Carrier)
12 2
In conventional AM a carrier is transmitted.
Let ( ) ( ).
The AM signal is written as
( ) cos 2 ( )cos 2 ( ) cos 2
Taking the Fourier transform gives
( ) ( ) ( ) (
AM C C C
AM C C CA
m t M f
t A f t m t f t A m t f t
t M f f M f f f f
) ( )
where we require ( ) 0
Cf f
A m t
Baseband
Carrier
AM Modulation -- Radio 46
Superheterodyne Receiver is Widely Used
AM radio receiver:
This is a very widely used topology in communication receivers.
AM Modulation -- Radio 47
Elenco AM/FM Dual-Radio Receiver Kit (Model AMFM108CK)
http://www.elenco.com/product/productdetails/radio_kits=MTc=/am--fm_radio_kit_(transistor)=NzE=
AM Modulation -- Radio 48
Single Sideband (SSB)
DSB-SC is spectrally inefficient because it uses twice the bandwidth of the message. The message uses bandwidth B but broadcast bandwidth 2B.
The signal can be reconstructed from either the upper sideband (USB) or the lower sideband (LSB).
SSB transmits a bandpass filtered version of the modulated signal.
Upper & Lower Bands
AM Modulation -- Radio 49
Single Sideband (SSB)
Multiplication of a USB signal by cos(ct) shifts the spectrum to left and right.
AM Modulation -- Radio 50
Phase-Shift Method to Generate SSB
( ) ( )cos( ) ( )sin( )
where minus sign applies to USB
and plus sign applies to the LSB.
( ) is ( ) phase delayed by - /2
SSB C h C
h
t m t t m t t
m t m t
See next slide
f
2
2
( )h f
AM Modulation -- Radio 51
Note on Quadrature Phase-Shift (/2)
-/2
Step 1 – Start with cos(t); then change phase by -/2.
Step 2 – The point at -/2 is now moved to the origin.
cos(t)
sin(t)
-/2 -/2 -/2 -/2
cos(t) sin(t) -cos(t) -sin(t) cos(t)
Reference:
AM Modulation -- Radio 52
Review: Spectral Lines for Sine and Cosine Signals
Example of a 90o phase shift
cos(t)
sin(t)
Time domain Frequency domain
AM Modulation -- Radio 53
Pulse Amplitude Modulation (PAM) – A Digital Signal
How is PAM in digital communication is similar to AM in analog communication?
We will see that modulation for analog is essentially identical To modulation in the digital communications.
1 0 0 1 0 1 0
AM Modulation -- Radio 54
Questions
?