ABSTRACT - Nc State University · module, low noise amplifier, mixer, and filters are mergeinto one...

ABSTRACT

HEO, SEUNG KYUN. The Performance of Passive Lumped Element. (Under the direction of Dr. Michael B. Steer).

Lumped elements are the most widely used passive components in Radio Frequency

(RF) circuits. The characteristics vary over frequency, however, limiting their application.

This limitation stems from the physical dimensions of lumped elements, which are, in

general, 0603 (i.e. 3 mm by 1.5 mm), 0402 (i.e. 2 mm by 1 mm), and 0201 (i.e. 1 mm by 0.5

mm) in size in order to avoid the phase shift between the input and the output. By examining

the quality factor and self-resonant frequency, the performance of lumped elements can be

quantified. The quality factor contains the energy storing and dissipation terms, which vary

according to frequency. This quality factor can be obtained using the S-parameters of lumped

elements.

It is difficult to obtain accurate measurements of a non-coaxial packaged devices such

as a lumped inductor, because it cannot be measured using a wide band measurement system.

A Print Circuit Board (PCB) fixture is thus considered to connect a device under test to 50

ohm connectors, and the effects of the fixture are then removed by performing a standards

calibration. The combination of port extension and calibration using a manufacturer’s

calibration kit is employed to collect one-port S-parameters. The best result is achieved using

an SMA fixture that has a short line and good impedance matching.

This thesis presents an extraction method to derive the quality factor of lumped

elements, and the quality factor is obtained using one-port S-parameters.

The Performance of Passive Lumped Element

by SeungKyun Heo

A thesis submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the degree of

Master of Science

Electrical Engineering

Raleigh, North Carolina

2010

APPROVED BY:

_______________________________ ______________________________ Professor Michael B. Steer Professor Paul D. Franzon Committee Chair ________________________________ Professor David Schurig

ii

DEDICATION

This dissertation is dedicated to my wife, Mi-Young Kim, and to my parents in Korea.

iii

BIOGRAPHY

Seung-Kyun Heo was born on 4th August, 1977 in Korea. He received the Bachelor

of Science degree in Electrical and Computer Engineering from Chung-Ang University

located in Seoul, Korea, in 2003. He began his master degree in the Electrical and Computer

Engineering Department at North Carolina State University in Raleigh, NC, in 2008. From

2003 to 2007, he worked as an RF engineer in Samsung Electronics Co., Suwon, Korea, and

from June 2009 to January 2010 he worked as an intern engineer in RFMD, Greensboro, NC.

His current interest is focused in the Field of RF circuit design.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................................ v LIST OF FIGURES ..............................................................................................................vi CHAPTER 1 Introduction ................................................................................................... 1

1.1 Motivation ...............................................................................................................1 1.2 Contribution.............................................................................................................2 1.3 Thesis Organization .................................................................................................3

CHAPTER 2 Basic Characteristic of Lumped Elements ...................................................... 4 2.1 Introduction .............................................................................................................4 2.2 Basic Parameters ......................................................................................................4 2.3 Quality Factor ..........................................................................................................8

2.3.1 Definition of Quality Factor ..........................................................................8 2.3.2 Effect of Quality Factor in an RF Circuit ..................................................... 10 2.3.3 Extraction of the Quality Factor................................................................... 11

2.4 Self Resonant Frequency........................................................................................ 13 2.5 Summary ............................................................................................................... 13

CHAPTER 1 Measurement Method .................................................................................. 17 3.1 Introduction ........................................................................................................... 17 3.2 Calibration ............................................................................................................. 18

3.2.1 Errors in VNA Measurement ....................................................................... 18 3.2.2 Errors Characteristic by Fixture Measurements ........................................... 19 3.2.3 SOLT Calibration ........................................................................................ 20 3.2.4 TRL Calibration .......................................................................................... 22 3.2.5 Port Extension ............................................................................................. 23 3.2.6 Time Gating ................................................................................................ 23

3.3 Quality Factor from Two-Port S-parameters ........................................................... 24 3.5 Summary ............................................................................................................... 28

CHAPTER 4 Measurement Results ..................................................................................... 31 4.1 Introduction ........................................................................................................... 31 4.2 One-Port S-Parameter Results ................................................................................ 32 4.3 Two-Port S-Parameter Results from Manufacturer ................................................. 34 4.4 Summary ............................................................................................................... 36

CHAPTER 5 Conclusions ................................................................................................... 38 5.1 Conclusions ........................................................................................................... 38 5.2 Future Work .......................................................................................................... 39

APPENDIX ......................................................................................................................... 40 Appendix A: Plot of Measurement Result .................................................................... 41

v

LIST OF TABLES

Table 2.1 Basic parameters of resistor ................................................................................... 5 Table 2.2 Critical parameter by material [10][17] .................................................................. 6 Table 2.3 Basic parameters of capacitors ............................................................................... 7 Table 2.4 Basic parameters of inductors ................................................................................ 8 Table 3.1 Summary of quality factor calculation .................................................................. 28 Table 4.1 TOKO inductor one-port quality factor and SRF measurement result ................... 33 Table 4.2 Johanson capacitor one-port SRF measurement result .......................................... 33 Table 4.3 Panasonic resistor one-port measurement result ................................................... 34 Table 4.4 Johanson capacitor two-port SRF measurement result .......................................... 35 Table 4.5 TOKO inductor two-port Q and SRF measurement result .................................... 35 Table 4.6 Panasonic resistor two-port measurement result ................................................... 36

vi

LIST OF FIGURES

Figure 1.1 RF block of LG300G ............................................................................................ 1 Figure 2.1 Relationship between I and V in a capacitor ......................................................... 5 Figure 2.2 Series RLC circuit and parallel RLC circuit .......................................................... 8 Figure 2.3 Common source amplifier .................................................................................. 10 Figure 2.4 Resonant circuit method ..................................................................................... 11 Figure 2.5 Reflection coefficient ......................................................................................... 12 Figure 3.1 DUT with fixture ................................................................................................ 19 Figure 3.2 Through standard S11,S22 .................................................................................. 20 Figure 3.3 User calibration kit ............................................................................................. 21 Figure 3.4 12-terms error model [2] ..................................................................................... 22 Figure 3.5 Port extension method ........................................................................................ 23 Figure 3.6 Time domain reflection response of a DUT with fixture ..................................... 24 Figure 3.7 ABCD parameter of series impedance ................................................................ 25 Figure 3.8 One-port VNA error model [5] [6] ...................................................................... 26 Figure 3.9 SMA connector fixture ....................................................................................... 28 Figure 4.1 Quality factor of Johanson capacitor [2] ............................................................. 31 Figure 4.2 SRF of Johanson capacitor [2] ............................................................................ 32 Figure A.1 Inductance and phase of impedance ................................................................... 42 Figure A.2 Quality factor of 2.2 nH inductor ....................................................................... 42 Figure A.3 Inductance and phase of impedance ................................................................... 43 Figure A.4 Quality factor of 3.3 nH inductor ....................................................................... 44 Figure A.5 Inductance and phase of impedance ................................................................... 44 Figure A.6 Quality factor of 6.8 nH inductor ....................................................................... 44 Figure A.7 Inductance and phase of impedance ................................................................... 45 Figure A.8 Quality factor of 10 nH inductor ........................................................................ 45 Figure A.9 Inductance and phase of impedance ................................................................... 46 Figure A.10 Quality factor of 33 nH inductor ...................................................................... 46 Figure A.11 Inductance and phase of impedance ................................................................. 47 Figure A.12 Quality factor of 56 nH inductor ...................................................................... 47 Figure A.13 Inductance and phase of impedance ................................................................. 48 Figure A.14 Quality factor of 100 nH inductor .................................................................... 48 Figure A.15 Inductance and phase of impedance ................................................................. 49 Figure A.16 Quality factor of 270 nH inductor .................................................................... 49 Figure A.17 Capacitance and phase of impedance ............................................................... 50 Figure A.18 Quality factor of 2.2 pF capacitor ..................................................................... 50 Figure A.19 Capacitance and phase of impedance ............................................................... 51 Figure A.20 Quality factor of 3.3 pF capacitor ..................................................................... 51 Figure A.21 Capacitance and phase of impedance ............................................................... 52 Figure A.22 Quality factor of 10 pF capacitor...................................................................... 52

vii

Figure A.23 Capacitance and phase of impedance ............................................................... 53 Figure A.24 Quality factor of 15 pF capacitor...................................................................... 53 Figure A.25 Capacitance and phase of impedance ............................................................... 54 Figure A.26 Quality factor of 33 pF capacitor...................................................................... 54 Figure A.27 Capacitance and phase of impedance ............................................................... 55 Figure A.28 Quality factor of 47 pF capacitor...................................................................... 55 Figure A.29 Capacitance and phase of impedance ............................................................... 56 Figure A.30 Quality factor of 82 pF capacitor...................................................................... 56 Figure A.31 Capacitance and phase of impedance ............................................................... 57 Figure A.32 Quality factor of 10 Ω resistor.......................................................................... 57 Figure A.33 Resistance, phase of impedance, and reactance ................................................ 58 Figure A.34 Quality factor of 39 Ω resistor.......................................................................... 58 Figure A.35 Resistance, phase of impedance, and reactance ................................................ 59 Figure A.36 Quality factor of 68 Ω resistor.......................................................................... 59 Figure A.37 Resistance, phase of impedance, and reactance ................................................ 60 Figure A.38 Quality factor of 200 Ω resistor ........................................................................ 60 Figure A.39 Resistance, phase of impedance, and reactance ................................................ 61 Figure A.40 Quality factor of 300 Ω resistor ........................................................................ 61 Figure A.41 Resistance, phase of impedance, and reactance ................................................ 62 Figure A.42 Quality factor of 560 Ω resistor ........................................................................ 62 Figure A.43 Resistance, phase of impedance, and reactance ................................................ 63 Figure A.44 Quality factor of 1 kΩ resistor.......................................................................... 63 Figure A.45 Resistance, phase of impedance, and reactance ................................................ 64 Figure A.46 Quality factor of 2 kΩ resistor.......................................................................... 64 Figure A.47 Resistance, phase of impedance, and reactance ................................................ 65 Figure A.48 Quality factor of 3 kΩ resistor.......................................................................... 65

1

CHAPTER 1 Introduction

1.1 Motivation

Lumped elements, such as inductors, capacitors, and resistors, are the most common

and important components in radio frequency (RF) and microwave circuits. To design RF

circuits correctly and efficiently, knowledge about the lumped elements is essential. Over the

last few decades suppliers have been able to meet this demand by overcoming RF circuit

performance limitations. Lumped elements, however, cannot always be applied in high

frequency applications because of variations in their characteristics. Figure 1.1 shows the RF

section of a mobile handset. Most of the parts, such as a switching module, power amplifier

module, low noise amplifier, mixer, and filters are merged into one package with the

exception of the lumped elements. Lumped elements none the less are still widely used in

biasing and matching networks because of their advantages including small size and low loss.

Figure 1.1 RF block of LG300G

Lumped elements are not the core part of an RF circuit. However, they constitute a

basic block of a big module. A robust system can be built by using high performance

elements that exhibit low variation over temperature, time, frequency, and in the biasing

environment. Characteristics that vary in frequency are often significant factors in RF

2

circuits. Identifying the quality factor and Self-Resonant Frequency (SRF) is useful in

defining and understanding the characteristics of lumped elements over frequency. The

quality factor contains the energy storing and dissipation terms, which are vary by frequency,

and this characteristic affects the performance of the circuit. If a high quality factor inductor

is used as the RF choke in a bias circuit, the gain of the amplifier can be improved. However,

a high quality factor does not always mean high performance. A high performance quality

factor varies according to the purpose of the circuit in which lumped elements are used. By

examining the characteristics of lumped elements over frequency, the lumped elements can

be better understood.

1.2 Contribution

Numerous articles about enhancing the performance of lumped elements have been

published. However, it is difficult to find recent articles that focus on characterizing the

lumped element itself. It is useful, therefore, to investigate the parameters of lumped

elements, especially their frequency-dependent characteristics. The starting point in RF

circuit design is understanding and knowing the limitation of lumped elements. This thesis

focuses on the characterization of lumped element parameters and establishing RF

measurement method. Finally, measurements are taken to obtain the quality factor and SRF

of a number of lumped element components. This thesis lays out the RF measurement

approach. Many data sheets of lumped element do not contain the quality factor over

frequency. By measuring major commercial lumped elements under the same testing

conditions, an understanding of the frequency-dependant characteristics of lumped elements

3

can be acquired. This thesis presents the performance of lumped elements over frequency

extended from S-parameter.

1.3 Thesis Organization

Chapter 2 reviews the basic parameters of lumped elements and the effects of

parasitics, and investigates the quality factor and SRF using S-parameters. Chapter 3 presents

a way to remove the error that is caused in using the vector network analyzer (VNA), which

uses a fixture, and method to obtain the quality factor using the S-parameters of lumped

elements. Chapter 4 summarizes the measurement results.

4

CHAPTER 2 Basic Characteristic of Lumped Elements

2.1 Introduction

The performance of lumped elements has been improved through invention and

applying numerous methods. Many manufacturers have tried to reduce the effects of

parasitics on the ideal inductance, capacitance, and resistance. Lumped elements have a

frequency limitation because of their dimensions and parasitics. Generally, the dimensions of

a lumped element should be smaller than λ/20 to guarantee phase equality at the input and

output ports. In spite of this problem, lumped elements are used widely because of their small

size, wide bandwidth, and low cost. Lumped elements have a large number of applications

such as impedance matching, DC blocking, RF chocking, bypass circuit, and degeneration in

RF circuit. The characteristic parameters of lumped elements must be known in order to use

lumped elements correctly and efficiently. In this chapter the basic parameters of lumped

elements are reviewed including quality factor (Q) and self resonant frequency (SRF).

2.2 Basic Parameters

Resistors are used in lossy impedance matching networks, attenuators, damping

resistors, and termination circuits. The most common resistor is a tick film resistor. When a

resistor is used as an RF component, the thermal noise from the resistor should be

considered. Because of this thermal noise, a resistor is rarely used in an RF matching

network. A resistance value can be calculated using sheet resistance with physical

dimensions. Table 2.1 shows the basic parameters of a resistor.

5

Table 2.1 Basic parameters of resistor.

Parameter Description

Power rating Maximum power that guarantees the basic characteristic and

reliability.

Maximum overload voltage Maximum voltage that can applied for 5 seconds.

Resistance tolerance Variation of the resistance value.

Temperature coefficient of

resistance (TCR) Variation of the degree of resistance value over temperature.

Operating temperature range Temperature range that guarantees the performance.

Rated current Continuous maximum current allowed.

A capacitor stores energy in an electric field. A typical unit range for a lumped

capacitor used in RF and microwave circuits is from picofarads to microfarads. The

impedance of an ideal capacitor can be expressed as 1jωC

. The impedance of the capacitor

contains ‘-j’ terms, which refers to the current leading the voltage by 90 degrees. This basic

concept is useful when a lumped element is applied to an RF circuit to cancel out the effects

of reactance. By using this concept, the phase relationship between the current and the

voltage in the RF circuit can be predicted easily.

Figure 2.1 Relationship between I and V in a capacitor.

0 2 4 6 8 10 12 14 -1 -0.8 -0.6 -0.4 -0.2

0 0.2 0.4 0.6 0.8

1

Time

I V

Am

plitude

I

V

j

-j

-1 1

6

Parameters such as the dielectric constant, break-down voltage, temperature

coefficient, insulation resistance, and dissipation factor determine the basic performance of a

capacitor [14]. Table 2.2 shows the characteristics of a capacitor for several dielectric

materials, which serve as the dominant performance determining factor of a capacitor. For

example, power loss in a capacitor comes from leakage of current and dissipation of power in

the dielectric. Furthermore, the temperature variation characteristic is also affected by the

dielectric constant. The NP0 material has the lowest dielectric constant has an advantage in

terms of temperature variation and power loss. However, high capacitance values cannot be

obtained by using NP0 material. To obtain a high capacitance value, a high dielectric

constant material is needed, which results in large temperature variations and low efficiency.

The appropriate tolerance to guarantee the performance for capacitance in an RF matching

circuit is ±5%. Table 2.3 shows the basic parameters of a capacitor.

Table 2.2 Critical parameter by material [10] [17].

Material Dielectric Constant % Capacitance Change Dissipation Factor

NP0 15-100 < 0.4% (-55 to 125C) 0.1%

X7R 2000-4000 +/-15% (-55 to 125C) 3.5%

X5R +/-15%(-55 to 85C) 5%

Y5V >16000 Up to 82% (-30 to 85C) 9%

7

Table 2.3 Basic parameters of capacitors.


Dielectric constant Constant factor of material used for dielectrics.

Category temperature range Operating temperature.

Rated voltage Maximum voltage can be applied.

Rated current Maximum current can be applied.

Capacitance tolerance Variation of capacitance value.

Withstand voltage Voltage that a capacitor can endure for a short time

(above rated voltage).

Dissipation factor The ratio of loss resistance to capacitance.

Insulation resistance DC resistor (related to leakage current).

An inductor is used as an RF choke in the bias circuit, and part of the matching

network. The current flowing through a line generates magnetic field, so that a single line has

inductance. For example, a typical bond wire has around 1 nH of inductance. The voltage

across an inductor leads the current by 90 degrees. Table 2.4 shows the basic characteristics

of an inductor.

Table 2.4 Basic parameters of inductors.


Maximum current rating Maximum current can be applied.

Maximum power rating Maximum power can be applied.

Operating temperature range Temperature range that guarantees the performance.

Temperature coefficient of inductance Inductance variation over temperature.

Time constant Voltage charge time in an inductor.

8

2.3 Quality Factor

2.3.1 Definition of Quality Factor

Most literature sources cite the definition of the quality factor as “The definition of

quality factor (Q) is 2π times the ratio of energy stored in a system to the energy dissipated

per cycle” [2] [3] [4].

QQ = 2πTotal Energy Stored

Energy Loss per Cycle = ω

Max Energy StoredAverage Power Loss

(Equation 2-1)

This definition of a dimensionless quality factor can be applied to all energy stored systems.

AC

C

LR

i

AC CLGV

Figure 2.2 Series RLC circuit and parallel RLC circuit.

The definition of quality factor can be applied to a simple series RLC:

Q = 2π12 Li2

12 Ri2T

= 2πfLR =

ωLR =

XL

R (Equation 2-2)

Similar to Equation 2-2, a parallel RLC circuit quality factor is

Q = 2π12 CV2

12 GV2T

= 2πfCG =

ωCG =

1ωGL =

RXC

(Equation 2-3)

9

The loss of lumped elements can be determined by observing the quality factor. In

reality, the loss of lumped elements varies by frequency, so it is not possible to calculate the

loss using a multimeter. The loss which varies with frequency is due to radiation and skin

effect. In general a high quality factor value means less loss and more energy stored. In a

reactive circuit, the ratio of the reactance in Ωs to the resistance in Ωs is defined as the

quality factor. The quality factor of an inductor can be represented using Equation 2-1 [5].

This general representation of a quality factor is sufficient for practical application.

Y11Q = ωMax Energy StoredAverage Power Loss

≅ 2ω(|W m| − |W e|)

Power Loss = −

Im|Y11|Re|Y11| (Equation 2-4)

This definition can be applied when the operating frequency is much lower than the self-

resonant frequency. In a filter, the quality factor is usually taken as the ratio of the center

frequency to the bandwidth [1] and represents the sharpness of the response.

Q = f0∆f (Equation 2-5)

Where f0 is resonant frequency and ∆f is 3dB bandwidth.

The quality factor of a lumped element is referred to as the unloaded quality factor.

The unloaded quality factor is the quality factor of a component or device that does not have

an external source and load. This concept considers only the ratio of the reactive part and

resistive part of the network itself. The loaded quality factor is affected by the choice of load

values and bandwidth. The unloaded quality factor of a lumped element is measured in this

thesis. In a resonant circuit, the quality factor is affected by load conditions rather than the

quality factor of the component itself.

10

2.3.2 Effect of Quality Factor in an RF Circuit

The quality factor is a frequency-defendant parameter and thereby affects RF circuits.

An inductor is used widely as an RF choke in amplifier bias circuits. Figure 2.3 shows a

simple common source Low Noise Amplifier (LNA) structure. Sufficient gain and input

impedance cannot be obtained for a LNA using a single common source amplifier; however,

it is sufficient for observing the effect of an inductor RF choke. The gain of an LNA is

|Av| = gm 1

Q2RD +

1jωLd

+ 1

RL

-1

(Equation 2-6)

Where gm is the transconductance of M1.

The gain of the LNA is proportional to the quality factor of Ld. To maximize the gain of the

LNA, a high quality factor RF choke inductor should be used.

Vin

Vout

RL

LdRd

Ld

M1

S

G

Rd

Ld RLgmVgs

+

-

Vgs

D Vout

Figure 2.3 Common source amplifier.

11

2.3.3 Extraction of the Quality Factor

The quality factor can be extracted by applying its definition to the circuit or

component. One of the oldest and most common methods used is a Q-meter measurement. A

Q-meter can measure the quality factor using a resonant circuit. This method is implemented

by applying the specified frequency current source to a DUT and a variable capacitor. Then

the maximum voltage across a variable capacitor, when its value is adjusted, is measured.

The reactance of the DUT is derived from the maximum voltage. Figure 2.5 shows this

resonant circuit method.

V C

RDL(XD)

DUT

Milivoltmeter

Figure 2.5 Resonant circuit method.

Determining the quality factor from the critical point method using the equivalent model and

impedance locus is also possible [15]. The quality factor is the ratio of the reactive energy

stored to the dissipated energy. In the case of an inductor, the reactive energy stored is the

difference between the magnetic energy and the electric energy. The quality factor is then

derived using this concept.

12

Lumped Inductor

ZL

+ +

--

V1 V2

in

I1 I2

ΓLΓ

Figure 2.6 Reflection coefficient.

This general definition of quality factor,𝑠𝑠Q= Im|Z|Re|Z|

, is sufficient for lumped element

measurements since the operating frequency is below the self resonant frequency. From the

general definition of quality factor, the quality factor can be obtained in terms of impedance.

The impedance of a lumped element can be obtained by measuring the input impedance of

the lumped element while placing a perfect short at the output. In this case, 𝑆𝑆11 is the

reflection coefficient and can be converted to the input impedance. By using one port

measurement with a short at the output, the quality factor can be generated. In terms of two-

port S-parameter, the input impedance of a network can be derived:

Γin = S11 + S12S21ΓL

1 − S22ΓL = S11 −

S12S21

1 + S22 (Equation 2-7)

Zin = 501 − Γin

1 + Γin = R + jX (Equation 2-8)

Z = Zin = R + jX (Equation 2-9)

Q = |X|R (Equation 2-10)

Where Load is a short (ΓL = −1).

If the load is a short, the input impedance is considered to be the impedance of the

network. Equations 2-7 to 2-10 show the derivation of the quality factor using S-parameter.

13

One of the advantages of using S-parameter is that it is easy to obtain data up to high

frequencies. For example, the Anritsu ME7828A VNA can measure up to 100 GHz. Also,

they can be converted to other parameters such as Z-parameter, Y-parameter, and ABCD-

parameter easily.

2.4 Self Resonant Frequency

A lumped element has parasitics because of the not insignificant physical dimensions.

If a lumped element has large dimensions, it has more parasitic characteristics and a lower

SRF. The effects of the parasitic capacitance and inductance increase as the operating

frequency increasing. The parasitic capacitance and inductance effects are dominant at

frequencies above the SRF. A lumped element must be used below the SRF to guarantee

nominal performance. The SRF can be determined by measuring the S-parameter. The point

at which the sign of the imaginary part of the impedance is changed is the SRF of the lumped

element. By measuring the S21, the SRF also can be found.

2.5 Summary

The basic parameters of lumped elements and the key parameters of an RF circuit

were reviewed in this chapter. Because of their benefits, lumped elements are used widely.

However, parasitics, which stem from the physical dimensions of lumped elements, limit

their operating frequency. These parasitics introduce loss and affect the characteristics of the

lumped elements over frequency. To characterize their effects the quality factor and self

resonant frequency are used. The definition of quality factor represents the ratio of power

http://www.us.anritsu.com/products/ME7828A_VectorStar-Broadband-VNA_ARSPG_ARQQSidZ1013.aspx

14

storage to power loss in a network, and the SRF indicates the frequency limitations of the

lumped element. The performance of the RF circuit, such as gain and frequency selectivity,

varies according to the quality factor of lumped elements. It was shown that the quality factor

can be generated using measured S-parameters.

15

REFERENCES

[1] I. J. Bahl, Lumped elements for RF and microwave circuits, Artech House, 2003.

[2] M. Sucher, Handbook of microwave and measurements, Polytechnic Press of the

Polytechnic Institute of Brooklyn, 1963.

[3] M. B. Steer, Microwave and RF Design: A Systems Approach, SciTech Publishing, 2010.

[4] D. M. Pozar, Microwave Engineering, 3rd ed. John Wiley & Sons, Inc., 2005.

[5] K. O, “Estimation methods for quality factors of inductors fabricated in silicon integrated

circuit process technologies,” IEEE J. Solid-State Circuits, vol. 33, pp. 1249–1252, Aug.

1998.

[6] H. Jiang, Y. Wang, J. A. Yeh, and N. C. Tien, “On-chip spiral inductors suspended over

deep copper-lined cavities,” IEEE Trans. Microwave Theory Tech., vol. 48, pp. 2415–2423,

Dec. 2000.

[7] Y. K. Koutsoyannopoulos and Y. Papananos, “Systematic analysis and modeling of

integrated inductors and transformers in RF IC design,” IEEE Trans. Circuits System II, vol.

47, pp. 699–713, Aug. 2000.

[8] T. S. Horng, K. C. Peng, J. K. Jau, and Y. S. Tsai, “S-parameter formulation of quality

factor for a spiral inductor in generalized two-port configuration”, IEEE Trans. Microwave

Theory Tech., vol. 51, pp. 2197–2202, Nov. 2003.

[9] C. P. Yue and S. S. Wong, “On-chip spiral inductors with patterned ground shields for Si-

based RF IC’s”, IEEE J. Solid-State Circuits, vol. 33, pp. 743–752, May. 1998.

16

[10] Johanson Dielectrics, “Basics of Ceramic Chip Capacitors”,

http://www.johansondielectrics.com/technical-notes/product-training/basics-of-ceramic-chip-

capacitors.html.

[11] K. Naishadham and T. Durak, “Measurement-based closed-form modeling of surface-

mounted RF components”, IEEE Trans. Microwave Theory Tech., vol. 50, pp. 2276–2286,

Oct. 2002.

[12] L. F. Tiemeijer, D. Leenaerts, N. Pavlovic, and R. J. Havens, “Record Q spiral inductors

in standard CMOS”, in Int. Electron Devices Meeting Tech. Dig., 2000, pp. 40.7.1–40.7.3,

Dec. 2001.

[13] R. K. Ulrich, Integrated Passive Component Technology, NJ: Wiley, 2003.

[14] J. G. Webster, Electrical Measurement, Signal Processing, and Displays, Boca Raton:

CRC Press, 2004.

[15] P. Wang, L. H. Chua, D. Mirshekar-Syahkal, “Accurate characterization of low-Q

microwave resonator using critical-points method”, IEEE Trans. Microwave Theory Tech.,

vol. 53, pp. 349–353, Jan. 2005.

[16] E. Sun, S. Chao , “ Unloaded Q measurement-the critical points method”, IEEE Trans.

Microwave Theory Tech., vol. 43, pp. 1983–1986, Aug. 1995.

[17] ATC capacitor, “Capacitor Dielectric Characteristics”,

http://www.atceramics.com/pdf/technotes/capacitor_dielectric.pdf.

http://www.johansondielectrics.com/technical-notes/product-training/basics-of-ceramic-chip-capacitors.html

http://www.johansondielectrics.com/technical-notes/product-training/basics-of-ceramic-chip-capacitors.html

http://ieeexplore.ieee.org.www.lib.ncsu.edu:2048/search/searchresult.jsp?searchWithin=Authors:.QT.Peng%20Wang.QT.&newsearch=partialPref

http://ieeexplore.ieee.org.www.lib.ncsu.edu:2048/search/searchresult.jsp?searchWithin=Authors:.QT.%20Lye%20Heng%20Chua.QT.&newsearch=partialPref

http://ieeexplore.ieee.org.www.lib.ncsu.edu:2048/search/searchresult.jsp?searchWithin=Authors:.QT.%20Mirshekar-Syahkal,%20D..QT.&newsearch=partialPref

http://www.atceramics.com/pdf/technotes/capacitor_dielectric.pdf

17

CHAPTER 1 Measurement Method

3.1 Introduction

The most important part of taking RF circuit measurements is setting up the correct

test environment that can be calibrated to remove errors. This is a time-consuming aspect of

the RF measurement process. A Vector Network Analyzer (VNA) is the most suitable

instrument to use for RF measurements when a passive element is to be measured over

frequency. To measure the S-parameter of a lumped element, the interface between the

lumped element and the VNA must be provided. A suitable fixture must be found to provide

a connection to a non-coaxial device such as a lumped element. An ideal fixture is a material

having no loss, no electrical length, no reflection, and a wide frequency response. A fixture

should guarantee the bandwidth and offer low loss to provide accurate test results. In this

thesis, Printed Circuit Boards (PCB) and SMA connector fixtures are used.

To accurately measure the S-parameters, the effects of the fixture should be removed

by performing calibration fixture standards. The added fixture causes measurement problems

such as insertion loss, phase shift, and mismatch. For example, the transmission lines in a

PCB fixture and in a connector generate insertion loss and phase shift. The mismatch

problem occurs when the connections between the networks have different characteristic

impedance. Fixture error problems can be removed by performing a full calibration. Using a

Through-Reflection-Load (TRL) calibration, better source match and load match corrections

can be achieved than via a Short-Open-Load-through (SOLT) calibration because of the

capacitance variation found in an open standard. However, the SOLT calibration is applied

18

here instead of the TRL calibration because of the absence of TRL calibration standards; the

line standard cannot be implemented in the test fixture.

3.2 Calibration

3.2.1 Errors in VNA Measurement

Three major errors occur in VNA measurements [1], [5], [6]. Drift error occurs when

a test environment is changed. One such environmental variation factor is a change in

temperature. To reduce this effect, most of the laboratory environment contains equipment

that can maintain a stable temperature and humidity. Calibrations should be executed

regularly to minimize the effect of test environment variations. The second major source of

errors is random error. Errors from noise cannot be predicted and removed. A VNA is an

instrument that itself is a noise source, so VNA measurements are affected by such noise.

These errors can be reduced not by calibration but by increasing the number of times

measurements are taken. Third, systematic errors, such as mismatch, insertion loss, and phase

shift, are the dominant types of error in VNA measurement. The root causes of these

systematic errors are signal leakage and unwanted reflection. Such systematic errors could be

removed by using their repeatable characteristics. Systematic errors can be determined during

the calibration procedure. In this thesis, of the three types of common error, only systematic

errors are considered.

19

Figure 3.1 DUT with fixture.

3.2.2 Errors Characteristic by Fixture Measurements

The characteristic impedance of an instrument that is connecting to a lumped element

causes mismatch. If the reflection performance is measured, the reflection should be only

from the Device Under Test (DUT). However, a reflection from connector or trace line could

also occur, which causes measurement error. This error can be removed using a time gating

method. In this thesis, however, the time gating method cannot be applied, because a VNA

does not have a time gating function option. Figure 3.2 shows the input and output reflections

of the through standards used for two-port S-parameter measurements. A mismatch ripple is

evident at around 3.5 GHz. By getting rid of the gap that causes this mismatch reflection

between the SMA connector and PCB board fixture, the mismatch ripple is mitigated

slightly. However, the reduction in the ripple is not enough to obtain an accurate

measurement. This error can be removed using a time gating method that can be applied in a

window of the time domain.

The transmission lines in the fixture and connector generate insertion loss and phase

shift. Insertion loss and phase shift would be small if a short transmission line is used in a

fixture. To avoid these errors a fixture should maintain zero electrical length. However, it is

20

not possible to maintain a zero electrical length in real measurement. The trace line should be

short to minimize the phase shift if an accurate calibration is not possible.

Figure 3.2 Through standard S11, S22.

3.2.3 SOLT Calibration

The SOLT calibration method uses a 12-term error model, which is calculated by

measuring calibrations standards. To obtain the 12 unknown parameters, 12 measurements

are needed. In order to perform SOLT calibration for an extended reference plane, work for

this thesis required specialized fixture calibration standards unique to this study. Figure 3.3

shows the through board of the RF3025 from RF Micro Devices that is employed as the user

standard for the SOLT calibrations performed in this thesis. However, these user standards

could not predict the correct error terms that cause measurement error. The through should be

zero length. However, because the zero length could not be implemented, the through

standard has added length, and the short standard does not provide an ideal short. The load

must guarantee the broadband response. At the DUT reference point, two 100 Ω resistors

were used to reduce inductance. However, the load standard contains error at high frequency

because of the frequency variations of the resistor. These errors led to inaccurate calibration.

-100

-50

0

0 1000 2000 3000 4000 5000 6000

dB

Freq(MHz)S11

Thru Modified Thru-100

-50

0

0 1000 2000 3000 4000 5000 6000

dB

Freq(MHz)S22

Thru Modified Thru

21

Two-port calibration is also possible by using only Open-Short-Load (OSL) standards

calibration [3].

Each standard has its own characteristics. The short standard is a unity reflection with

a 180° phase shift. The short standard contains inductance and should be specified. A short

line interface is needed to reduce the inductance. The open standard is a unity reflection with

no phase shift. However, fringing capacitance generates the phase shift. This fringing

capacitance should be determined in order to insert the calibration standard data. The

characteristics of the fringing capacitance of the open standard can be generated by using a

suitably calibrated instrument. The characteristics of all the standards should be known in

order to execute the correct calibration. However, fringing capacitance varies by frequency,

so an SOLT calibration is useful only below 3 GHz.

Figure 3.3 User calibration kit.

Open Short

Load

Through

DUT

22

3.2.4 TRL Calibration

The TRL calibration method uses a 12-terms error model. By measuring through,

reflection, and line standard the error terms can be determined. The through standard is a

direct connection between Port 1 and Port 2 (S= 0 11 0

). the reflection standard is a short or

open response (S11=S22=Γshort or Γopen). The line is a short line inserted between Port 1 and

port 2 ( S= 0 e-βl

e-βl 0).

Figure 3.4 12-terms error model, after [2].

If the fixture is symmetric, the through-line (TL) calibration can be applied instead of

the TRL calibration. Short or open standard measurements can be obtained from through

measurements [4]. The advantage of TL calibration is that the random effect, which causes

glitches in measurements, of the arbitrary reflection standard can be removed. The reflection

23

of the short standard is derived from the S-parameter measurement of the through standard. A

detailed derivation is presented in [4].

Γshort = S11 Through − S21Through (Equation 3-1)

3.2.5 Port Extension

The port extension method is useful when calibration standards are difficult to

implement. This method cannot correct mismatch and losses. So, it is useful when a short

well-matched fixture is available. First, the coaxial reference plane should be a known plane

by performing a full 2-port calibration using manufacturer calibration standards. Phase shift

and added delay are corrected by doing the port extension of a short or open standard.

Figure 3.5 Port extension method.

3.2.6 Time Gating

The frequency domain can be converted to the time domain by using the inverse-

Fourier transform. If the through standard is measure using the VNA’s time domain setting,

DUT

2-Port calibration using manufacture Cal kit 2-Port port extension

24

more than one reflection can be observed. One reflection occurs from the DUT and the other

occurs from mismatch. These two reflections are illustrated in Figure 3.6. The first one is

from an SMA-transmission line connection, and the second one is from a DUT. So, only the

second response is the expected measurement. By capturing only the desired reflection, the

reflection from the mismatch error can be removed.

Figure 3.6 Time domain reflection response of a DUT with fixture.

3.3 Quality Factor from Two-Port S-parameters

Network parameters, such as the S-parameter, Z-parameter, Y-parameter, and ABCD-

parameters represent the characteristics of passive elements. If the two-port S-parameter of a

lumped element is measured, the quality factor of the lumped element can be generated. The

first step of the quality factor calculation is finding the impedance. From [2]

Yij = Ii

Vj (Vk = 0 for k ≠ j) (Equation 3-2)

“Yij can be determined by driving Port j with voltage Vj, short-circuiting all other

ports (so Vk=0 for k≠j), and measuring the short-circuit current at Port i” [2]. From this

definition Y11 is the admittance with an ideal short load at the output port; 𝑌𝑌11 is the

25

admittance of the input port while the output port is shorted to ground. As mentioned in

Chapter 2, S-parameters can be converted to Z-parameters, Y-parameters, and ABCD-

parameters. By converting the S-parameters to Y-parameters, the quality factor also can be

generated.

Y11 = (1 − S11)(1 + S22) + S12S21

(1 + S11)(1 + S22)− S12S21 (Equation 3-3)

𝑄𝑄Q Q = −Im|Y11|Re|Y11| (Equation 3-4)

Y11 B = Z0(1 + S11)(1 + S22)− S12S21

2S21 (Equation 3-5)

Y11Q=Im|B|Re|B| (Equation 3-6)

The impedance of the network can be derived from the ABCD parameter. Series impedance z

is the B of the ABCD parameter according to an ABCD parameter definition [7], see Figure

3.7.

Figure 3.7 ABCD parameters of a series impedance.

𝐴𝐴 = 1 𝐵𝐵 = 𝑧𝑧𝐶𝐶 = 0 𝐷𝐷 = 1

z 1 2

26

3.4 Quality Factor from One-Port S-Parameter

A one-port measurement is required if the characteristic of the DUT is determined

using only reflection. The error in one–port measurements can be represented using a three-

term error, see Figure 3.8. These error terms can be determined by examining the SOL

standards.

Figure 3.8 One-port VNA error model [5] [6].

By using a signal flow graph applied to the network in Figure 3.8:

S11M = EDF + S11ERF

1-S11ESF (Equation 3-7)

S11 = S11M − EDF

ESF(S11M − EDF) + ERF (Equation 3-8)

The three unknown term, EDF, ESF, and ERF, can be derived by measuring three calibration

standards, and measured value, S11M, convert to the actual value, S11, using Equation 3-8.

𝑆𝑆11𝑀𝑀 𝑆𝑆11

𝐸𝐸𝑅𝑅𝑅𝑅

𝐸𝐸𝐷𝐷𝑅𝑅 𝐸𝐸𝑆𝑆𝑅𝑅

1 Reference

27

In the case of an inductor, the stored reactive energy is the difference between

magnetic energy and electric energy. The quality factor is derived using this concept when

the load is an ideal short. The following calculation is derived from [6]:

Q = 2πPeak Magnetic Energy-Peak Electric Energy

Energy Loss per One Cycle

= 2π2×Wm,avg − 2×We,avg

Pl,avg×T =2ωWm,avg −We,avg

Pl,avg

=ImZinReZin where Zin=Z0

(1 + Γin)(1− Γin)

=Im(50× 1 + S11

1 − S11)

Re(50× 1 + S111 − S11

) (Equation 3-9)

So, the quality factor can be derived from a one-port S-parameter using an ideal short. To

obtain the one-port S-parameter of a lumped element, the manufacturer calibration standards

and port extension method are implemented in this thesis. The port extension is not a perfect

calibration method, so the direct SMA connector fixture is applied to minimize measurement

errors. As shown in Figure 3.9, the SMA connector fixture has a very short length and direct

connection to the DUT.

28

Figure 3.9 SMA connector fixture.

3.5 Summary

The test environment is the most important factor in obtaining accurate RF

measurements. Unknown terms and variations in the instruments should be removed. The

appropriate instrument to employ is the VNA to measure the characteristics of lumped

elements over frequency. Possible errors in VNA measurements include drift error, random

error, and systematic error. Several calibration methods, such as SOLT calibration, TRL

calibration, port extension, and time gating, are considered for making the VNA and fixtures

known terms. From the S-parameter, the quality factor can be determined. Table 3.1 presents

a summary of the quality factor calculation methods.

Table 3.1 Summary of quality factor calculation.

One-Port S-parameter Two-Port S-parameter (with virtual short load)

Using term Zin Zin Y11 B

Q factor Im|Zin|Re|Zin|

Im|Zin|Re|Zin| −

Im|Y11|Re|Y11|

Im|B|Re|B|

29

The best approach to obtaining a one-port S-parameter with the limited source

available is the combination of the port extension and manufacturer calibration kit. To

minimize measurement errors, a direct SMA connector fixture is applied. It has a very short

length and direct connection to the DUT.

30

REFERENCES

[1] Agilent, “In-fixture Measurements Using Vector Network Analyzers,” Application Note

AN 1287-9, 2006.

[2] Agilent, “Agilent Network Analysis Applying the 8510 TRL Calibration for Non-

Coaxial Measurement,” Product Note 8510-8AZ, 2006.

[3] Z. Y. Chen, Y. L. Wang, Y. Liu, and N. H. Zhu, “Two-port Calibration of test fixtures

with OSL method,” in International Conference on Microwave and Millimeter Wave

Technology Proceedings, pp. 138–141, 2002.

[4] M. B. Steer, S. B. Goldberg, G. Rinne, P. D. Franzon, I. Turlik, and J. S. Kasten,

“Introducing Through-Line Deembedding Procedure,” in 1992 IEEE MTT-S International

Microwave Symposium Digest, vol.3 pp. 1455–1458, 1992.

[5] L. F. Chen, Micorwave Electronics: Measurement and Materials Characterization,

Chichester: John Wiley & Sons, Ltd, 2004.

[6] J. M. Golio, The RF and Microwave Handbook, 2nd ed. CRC Press, 2008.

[7] M. B. Steer, Microwave and RF Design: A Systems Approach, SciTech Publishing, 2010.

31

CHAPTER 4 Measurement Results

4.1 Introduction

An Anritsu MS4623 VNA was used in this study to collect S-parameters up to 5 GHz.

To obtain two-port S-parameters, a user fixture, which provides the interface between the

lumped element and the VNA, was employed. Correct measurement result, however, could

not be achieved because of the inaccuracy of the user fixture calibration standards. The

proposed alternative method used was to obtain a one-port measurement, which combines

port extension and calibration using manufacturer’s calibration kit. To improve the

measurement accuracy, a SMA fixture, which has a short line and good impedance matching,

was used. A lumped element was soldered directly to the SMA connector. The quality factor

and SRF could then be obtained using one-port S-parameters and two-port S-parameters from

the manufacturer.

Figure 4.1 Quality factor of Johanson capacitor [2].

32

Figure 4.2 SRF of Johanson capacitor [2].

The part numbers for the lumped elements are TOKO LL1608FSL for the inductor,

Johanson 251R15S for the capacitor, and Panasonic ERJ-3GEYJ100 for the resistor. The size

of each lumped element is 1.6 × 0.8 mm.

4.2 One-Port S-Parameter Results

From one-port parameters, which were collected using a short load, the impedance

values of lumped elements are obtained, and the quality factor and SRF of the lumped

elements are obtained from their impedance value. Table 4.1 shows a summary of quality

factors obtained from one-port S-parameter measurements. Detailed measurement plots are

presented in Appendix A. Each capacitance, inductance, resistance, SRF, and quality factor

of the lumped elements is plotted and presented in Appendix A.

33

Table 4.1 TOKO Inductor one-port quality factor and SRF measurement results.

0603 Toko Inductor SRF(MHz) Quality Factor

100 MHz 300 MHz

500 MHz

800 MHz

1000 MHz

1800 MHz

2.2nH Data sheet 9100±15% 13 26.5 35.4 44.2 51.9 63.9

Measurement above 5000 6.469 32.765 29.732 48.698 53.038 42.082

3.3nH Data sheet 5800±15% 13.8 27.8 36 46.4 52.9 68

Measurement above 5000 7.271 32.494 28.032 43.966 40.799 41.539

6.8nH Data sheet 4700±15% 15.8 29.4 39 49.3 55.8 67.5

Measurement 4970 10.634 30.026 37.295 42.685 44.776 47.182

10nH Data sheet 4000±15% 17.3 29.3 38.6 48.1 53.8 56.7

Measurement 4060 13.436 35.263 40.47 43.162 44.069 41.005

33nH Data sheet 2000±15% 19.6 33.2 42.2 48 47.9 15.9

Measurement 2016 18.47 30.42 38.074 33.397 29.951 13.437

56nH Data sheet 1500±15% 21.5 31.7 38.6 38.6 33.5

Measurement 1455 19.532 25.67 32.146 26.901 20.204

100nH Data sheet 900±15% 20.5 35.5 39.1 20.4

Measurement 910 19.6 20.549 20.739 4.454

270nH Data sheet 470±15% 21.9 21.1

Measurement 430 19.476 10.728

Table 4.2 Johanson Capacitor one-port SRF measurement results.

0603 Johanson Capacitor

SRF(MHz)

2.2pF 3.3pF 10pF 15pF 33pF 47pF 82pF

4500 3500 2000 1600 1100 900 700

The measurement data presented in Table 4.2 are the measurement results obtained

from the Johanson 251R15S capacitors. These results do not include the quality factor results

because of instrument resolution problems. The instrumentation uncertainty of the MS4623 is

±0.15dB [1]. In the case of a high quality factor, that is, above 1000, the results can be

34

inaccurate due to this instrumentation uncertainty. For example, the quality factor of the

Johanson 3.3pF capacitor is about 3000 at 300 MHz, as shown in Figure 4.1. The Equivalent

Series Resistance (ESR) value is very low; a typical value of ESR is from 0.05 to 0.15. So,

the instrumentation uncertainty affects the measurement results, and the measurement results

of capacitor include the instrument error. The ripples caused by instrument error are shown in

the capacitor result plots presented in Appendix A.

Table 4.3 Panasonic resistor one-port measurement results

0603

Panasonic

Resistor

Quality Factor (at 1 GHz)

10 Ω 39 Ω 68 Ω 200 Ω 300 Ω 560 Ω 1000 Ω 2000 Ω 3000 Ω

0.7 0.15 0.075 0.025 0.06 0.15 0.3 0.6 1

Table 4.3 shows the quality factor value of the resistors at 1 GHz. Resistors have very

low quality factor values compare those of capacitors and inductors. Inductance is dominant

from 10 Ω to 68 Ω, and capacitance is dominant from 200 Ω to 3000 Ω as parasitics.

Capacitance parasitics values are 0.1 to 0.3 pF, and inductance parasitics values are around 1

nH. Most of the resistor manufacturers do not provide the quality factor values of their

resistors, so the results cannot be compared with the datasheet.

4.3 Two-Port S-Parameter Results from Manufacturer

To obtain the impedance value of lumped elements, two-port S-parameters are

converted to one-port S-parameters using a virtual short to ground plane. Errors that stem

from the calibration standards, however, affect the results, especially at high frequencies. So,

35

instead of the measurement data, S-parameters provided by the manufacturer are used to

compare the one-port and two-port measurement data. Table 4.4, Table 4.5, and Table 4.6

provide a summary of the inductor results obtained from the calculations.

Table 4.4 Johanson capacitor two-port SRF measurement results.

0603 Johanson Capacitor

SRF(MHz)

2.2pF 3.3pF 10pF 15pF 33pF 47pF 82pF

4000 3600 2000 1600 1200 1100 800

Table 4.5 TOKO inductor two-port Q and SRF measurement results.

0603 Toko Inductor SRF(MHz) Quality Factor

100 MHz 300 MHz

500 MHz

800 MHz

1000 MHz

1800 MHz

2.2nH Data sheet 9100±15% 13 26.5 35.4 44.2 51.9 63.9

Calculation above 6000 9.493 15.992 22.59 29.418 31.493 39.069

3.3nH Data sheet 5800±15% 13.8 27.8 36 46.4 52.9 68

Calculation 5290 11.198 17.999 24.392 32.699 36.625 43.362

6.8nH Data sheet 4700±15% 15.8 29.4 39 49.3 55.8 67.5

Calculation 3850 11.975 21.619 30.031 38.985 42.513 40.708

10nH Data sheet 4000±15% 17.3 29.3 38.6 48.1 53.8 56.7

Calculation 2980 13.821 23.737 32.08 40.254 42.662 29.637

33nH Data sheet 2000±15% 19.6 33.2 42.2 48 47.9 15.9

Calculation 1570 16.903 30.154 36.574 34.386 25.237

56nH Data sheet 1500±15% 21.5 31.7 38.6 38.6 33.5

Calculation 1160 18.023 29.632 32.251 19.843 8.01

100nH Data sheet 900±15% 20.5 35.5 39.1 20.4

Calculation 820 20.875 31.083 26.546 1.825

270nH Data sheet 470±15% 21.9 21.1

Calculation 400 20.363 12.4

36

Table 4.6 Panasonic resistor two-port measurement results.

0603 Panasonic

Resistor

Quality Factor (at 1 GHz) 10 Ω 39 Ω 68 Ω 560 Ω 1000 Ω 3000 Ω

0.7 0.15 0.075 0.1 0.2 0.6

4.4 Summary

This chapter presents the quality factors and SRFs of lumped elements using S-

parameters. Several methods were applied to obtain the correct S-parameters of the lumped

elements. The two-port measurements, which were taken first, are not appropriate for

deriving the quality factor because of calibration standards errors. To overcome the error of a

fixture, a port extension and calibration using a manufacturer’s calibration kit were applied

for a one-port measurement. In the case of inductors, the measurement results match the

values in the data sheet very well. However, the instrumentation uncertainty affects the

results of capacitors that have low ESR values; the result, ripples are shown in the quality

factor plot.

37

REFERENCES

[1] Anritsu, “MS4622 A/B/C/D, MS4623, MS4624 A/B/C/D Vector Network Measurement

Systems,” 2006. Available at

http://www.us.anritsu.com/Downloads/Datasheet-Configuration%20Guide/MS462xASeries-

MS462xCSeries-ME7840A-ME7842B-ME7840/4-MS462xB/DSeries-

VariousWirelessBaseStationTransmitFrequencies_downloadmaster.aspx?fileName=11410-

00288.pdf&fileID=1270&fileType=12

[2] Johanson, “Capacitor Catalog,” Available at

http://www.johansontechnology.com/images/stories/catalog/JTI_MLCC_HighQ_2010-

04.pdf.

[3] Anritsu, “Inductor catalog,” Available at

http://www.toko.co.jp/products/pdf/inductors/ll1608-fsl.pdf.

http://www.us.anritsu.com/Downloads/Datasheet-Configuration%20Guide/MS462xASeries-MS462xCSeries-ME7840A-ME7842B-ME7840/4-MS462xB/DSeries-VariousWirelessBaseStationTransmitFrequencies_downloadmaster.aspx?fileName=11410-00288.pdf&fileID=1270&fileType=12






http://www.johansontechnology.com/images/stories/catalog/JTI_MLCC_HighQ_2010-04.pdf

http://www.johansontechnology.com/images/stories/catalog/JTI_MLCC_HighQ_2010-04.pdf

http://www.toko.co.jp/products/pdf/inductors/ll1608-fsl.pdf

38

CHAPTER 5 Conclusions

5.1 Conclusions

To observe the characteristics of lumped elements in terms of frequency change, the

quality factor, which represents the ratio of power storage to power loss in a network, is the

appropriate parameter. In this thesis, the quality factors of the lumped elements are derived

from one-port S-parameters. One-port S-parameters, which are useful in RF circuit analysis,

can be obtained over frequency using a VNA. A test fixture should be employed to provide

the interface between the DUT and the VNA, and the effects of the test fixture should be

removed using standard calibration. To minimize the errors caused by a port extension

method, the SMA connector is used which has a very short length and direct connection to

the DUT, is applied. Good measurement results for the inductors are achieved compared to

the resultant data in the data sheet. However, the results for the capacitors, which have low

ESR values show ripples in the quality factor plot. This error comes from instrumentation

uncertainty.

The most challenging part of this research was collecting accurate measurement data,

because the experiments were executed within a limited test environment. If TRL standards

could be implemented, then more accurate results could be achieved at high frequencies. The

quality factor and SRF of commercial lumped RF microwave elements are presented in this

thesis

39

5.2 Future Work

Two-port VNA measurement could not provide accurate data for this research due to

imperfect calibration standards. If correct user fixture calibration standards are employed,

correct two-port S-parameters of lumped elements can be obtained, and a comparison of the

calibration methods can then be exhibited. To apply the correct user fixture calibration

standards, new PCB fixtures or commercial fixture are needed. Experimental results show the

discrepancies among the data sheet data, especially in the case of the capacitor. Another

method should be considered. For instance, a resonant circuit method, which is based on the

resonant system with a variable impedance load, can be employed as the solution to measure

the high quality factors.

40

APPENDIX

41

Appendix A: Plot of Measurement Result

Inductance, capacitance, resistance, phase of impedance, and Q factor was plotted

using S-parameters of lumped elements. Each lumped element has two figures. Reactance

and phase of impedance were plotted in the upper figure and Q factor was plotted in the

lower figure.

42

1. Inductor

Figure A.1 Inductance and phase of impedance.

Figure A.2 Quality factor of 2.2 nH inductor.

0

10

20

30

40

50

60

70

80

90

100

0

1

2

3

4

5

6

7

8

9

10

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)

0603 Toko 2.2 nH Inductor (LL1608FSL)

InductanceDegree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter

2-Port S-Parameter from manufacturer

43



0

10

20

30

40

50

60

70

80

90

100

0

1

2

3

4

5

6

7

8

9

10

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)


Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter2-Port S-Parameter from manufacturer

44



0

10

20

30

40

50

60

70

80

90

100

0

2

4

6

8

10

12

14

16

18

20

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)


Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)



45


Figure A.8 Quality factor of 10 nH inductor.

-100

-80

-60

-40

-20

0

20

40

60

80

100

0

5

10

15

20

25

30

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)

0603 Toko 10 nH Inductor (LL1608FSL)

Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)



46

Figure A.9 Inductance and phase of impedance


-100

-80

-60

-40

-20

0

20

40

60

80

100

0

10

20

30

40

50

60

70

80

90

100

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)


Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)



47



-100

-80

-60

-40

-20

0

20

40

60

80

100

-10

10

30

50

70

90

110

130

150

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)


Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)



48



-100

-80

-60

-40

-20

0

20

40

60

80

100

0

50

100

150

200

250

300

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)


Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)



49



-100

-80

-60

-40

-20

0

20

40

60

80

100

0

50

100

150

200

250

300

350

400

450

500

0 1000 2000 3000 4000 5000 6000

Deg

ree

Indu

ctan

ce (n

H)

Freq (MHz)


Inductance

Degree

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Q F

acto

r

Freq (MHz)



50

2. Capacitor

Figure A.17 Capacitance and phase of impedance.

Figure A.18 Quality factor of 2.2 pF capacitor.

-100

-80

-60

-40

-20

0

20

40

60

80

100

0

1

2

3

4

5

6

7

8

9

10

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)

0603 Johanson 2.2 pF Capacitor (251R15S)

CapacitanceDegree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


51


Figure A.20 Quality factor of 3.3 pF capacitor.

-100

-80

-60

-40

-20

0

20

40

60

80

100

0

2

4

6

8

10

12

14

16

18

20

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)


Capacitance

Degree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


52


Figure A.22 Quality factor of 10 pF capacitor.

-100

-80

-60

-40

-20

0

20

40

60

80

100

0

5

10

15

20

25

30

35

40

45

50

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)

0603 Johanson 10 pF Capacitor (251R15S)

Capacitance

Degree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


53



-100

-80

-60

-40

-20

0

20

40

60

80

100

0

10

20

30

40

50

60

70

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)


Capacitance

Degree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


54



-100

-80

-60

-40

-20

0

20

40

60

80

100

0

10

20

30

40

50

60

70

80

90

100

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)


Capacitance

Degree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


55

Figure A.27 Capacitance and phase of impedance


-100

-80

-60

-40

-20

0

20

40

60

80

100

0

20

40

60

80

100

120

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)


Capacitance

Degree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


56



-100

-80

-60

-40

-20

0

20

40

60

80

100

0

20

40

60

80

100

120

140

160

180

200

0 1000 2000 3000 4000 5000 6000

Deg

ree

Capa

cita

nce

(pF)

Freq (MHz)


Capacitance

Degree

1

10

100

1000

10000

0 1000 2000 3000 4000 5000 6000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter


57

3. Resistor

Figure A.31 Resistance, phase of impedance, and reactance.

Figure A.32 Quality factor of 10 Ω resistor.

0

20

40

60

80

9.5

10

10.5

11

11.5

12

Deg

ree

Resi

stan

ce (o

hm)

0603 Panasonic 10 ohm Resistor (ERJ-3GEYJ100)

Resistance

Degree

0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

3

3.5

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)

InductanceCapacitance

0

1

2

3

4

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter

58



-10

0

10

20

30

40

38

39

40

41

42

Deg

ree

Resi

stan

ce (o

hm)


Resistance

Degree

0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

3

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.2

0.4

0.6

0.8

1

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter2-Port S-Parameter from …

59



0

5

10

15

20

66

67

68

69

70

71

72

Deg

ree

Resi

stan

ce (o

hm)


Resistance

Degree

0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

3

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.1

0.2

0.3

0.4

0.5

10 100 1000 10000

Q F

acto

r

Freq (MHz)



60



-20

-15

-10

-5

0

5

170

175

180

185

190

195

200

205

Deg

ree

Resi

stan

ce (o

hm)


ResistanceDegree

0

10

20

30

40

50

60

0

0.2

0.4

0.6

0.8

1

1.2

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.05

0.1

0.15

0.2

0.25

0.3

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter

61



-30

-25

-20

-15

-10

-5

0

5

0

50

100

150

200

250

300

350

Deg

ree

Resi

stan

ce (o

hm)


ResistanceDegree

0

10

20

30

40

50

60

0.0

1.0

2.0

3.0

4.0

5.0

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.1

0.2

0.3

0.4

0.5

0.6

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter

62



-50

-40

-30

-20

-10

0

10

0

100

200

300

400

500

600

700

Deg

ree

Resi

stan

ce (o

hm)


ResistanceDegree

0

10

20

30

40

50

60

70

0.0

1.0

2.0

3.0

4.0

5.0

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.2

0.4

0.6

0.8

1

1.2

10 100 1000 10000

Q F

acto

r

Freq (MHz)



63


Figure A.44 Quality factor of 1 kΩ resistor.

-70

-60

-50

-40

-30

-20

-10

0

10

0

200

400

600

800

1000

1200

Deg

ree

Resi

stan

ce (o

hm)


ResistanceDegree

0

5

10

15

20

25

30

35

0.00

1.00

2.00

3.00

4.00

5.00

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.5

1

1.5

2

10 100 1000 10000

Q F

acto

r

Freq (MHz)



64



-80

-60

-40

-20

0

20

0

500

1000

1500

2000

2500

Deg

ree

Resi

stan

ce (o

hm)


ResistanceDegree

012345678

0.00

1.00

2.00

3.00

4.00

5.00

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

0.5

1

1.5

2

2.5

3

10 100 1000 10000

Q F

acto

r

Freq (MHz)


1-Port S-Parameter

65



-100

-80

-60

-40

-20

0

20

0

500

1000

1500

2000

2500

3000

3500

Deg

ree

Resi

stan

ce (o

hm)


ResistanceDegree

0

2

4

6

8

10

12

14

0.00

1.00

2.00

3.00

4.00

5.00

0 1000 2000 3000 4000 5000 6000

Capa

cita

nce

(pF)

Indu

ctan

ce (n

H)

Freq (MHz)


0

1

2

3

4

5

10 100 1000 10000

Q F

acto

r

Freq (MHz)



ABSTRACT - Nc State University · module, low noise amplifier, mixer, and filters are mergeinto one...

Documents

Transcript of ABSTRACT - Nc State University · module, low noise amplifier, mixer, and filters are mergeinto one...