Master's Thesis in Electronics/Telecommunications

DEPARTMENT OF TECHNOLOGY AND BUILT ENVIRONMENT

C-BAND MICROWAVE OSCILLATOR

Maaz Rasheed

September 2008

Master's Program in Electronics/Telecommunications

Supervisor: Steffen Kirknes

Examiner: Olof Bengtsson

i

Abstract

The work focuses on the study, design and implementation of a C band Microwave

oscillator using coaxial resonators, for the transceiver used in wave radar. It involves

a literature study discussing different aspects of microwave oscillators, mainly the

shielding of the oscillators, frequency pulling due to load and supply pulling, tuning

range and the temperature performance of the oscillator. The study of the shielding

resulted in proposing a high quality metallic shield with high elastic modulus, high

strength and high density, as the wave radar will be a stationary, standalone system

and the weight of the shield is not a limiting factor. The metallic shield provides

better EMI and EMP performance than the carbon ferrites. The characterization of the

resonator is critical as a small mistake pulled the frequency about 300 MHz. This can

be achieved by careful design and measuring the resonator test circuits for one port.

The tuning range of the oscillator is important as the temperature, bias, and load

mismatches can increase or decrease the frequency of the oscillator. The varactor in

combination with a capacitor increases the tuning range to about 10 times. The high

reverse isolation of 47 dB is achieved by a passive attenuator and a buffer amplifier.

The temperature performance is also important and there was a 30 MHz variation in

frequency from 0 − 60𝑜 𝐶 , and the output power was between 3-4 dBm. The Load

puling was 1 MHz with a 12 dB return loss test setup for a phase change of 0 − 180𝑜 .

The phase noise was −98 𝑑𝐵𝑐/𝐻𝑧 at 100 𝑘𝐻𝑧 offset. Overall the coaxial resonator

oscillator proves to be a very good stable oscillator suitable for aerospace and ground

based industry.

ii

Acknowledgements

This Master’s thesis in Electronics/Telecommunications was conducted at Norbit AS,

Trondheim, Norway, which represents one of the largest RF and microwave

competence centre, in Nordic countries. The duration of this project is six months

from 1st March to 31

st August 2008.

First of all, I would like to thank my Supervisor, Steffen Kirknes for his guidance,

encouragement and support during this project. I would also appreciate all my

colleagues at Norbit for their continuous help and encouragement. Apart from

guidance, I was also given access to all the equipment and facilities at Norbit AS that

were essential for my thesis.

Special thanks go to the staff of ITB/Electronics, University of Gavle, Sweden with

my gratitude to Prof. Claes Beckman, Prof. Niclas Björsell, Olof Bengtsson, Per

Ängskog, Magnus Isaksson and Prof. Edvard Nordlander for their support during the

period of studies. I would like to appreciate all my good and kind friends in Gavle,

Sweden.

Finally I would like to express my gratitude to my parents, who have financed,

encouraged and helped me in my studies. Without their support, it was impossible for

me to come to Sweden and study this prestigious Master’s degree program.

iii

To my motherland, Pakistan!

To my Parents!

To my Wife!

iv

Table of Contents

Page No.

Chapter 1 Introduction………………………………………………. 1

1.1 Introduction…………….................................................................. 1

1.2 Susceptibility to Electromagnetic Fields and Shielding………........ 2

1.3 Tuning Range……………………………………………………… 5

1.4 Temperature Stability……………………………………………… 5

1.5 Frequency Pulling due to Load…………………………………….. 7

1.6 Frequency Pulling due to Supply…………………………………... 8

1.7 Thesis Outline……………………………………………………… 10

Chapter 2 Theory ……………………………………………………. 11

2.1 Theory of Oscillators…………………………………………….. 11

2.2 Microwave Oscillator Configurations…………………………… 11

2.3 Voltage Controlled Oscillators………………………………….. 12

2.4 Considerations for Oscillators…………………………………… 12

2.4.1 Phase Noise…………………………………………………… 12

2.4.2 Harmonic Suppression……………………………………..… 12

2.4.3 Spurious signals in the Oscillator Output……………………. 13

2.4.4 Post-tuning Drift……………………………………………... 13

2.4.5 Blocking or Reciprocal Mixing……………………………… 13

2.4.6 Linear Tuning characteristics………………………………... 14

2.5 Choice of the Active Device and Modeling …………………….. 14

2.6 Loaded Q…………………………………………………………. 15

Chapter 3 Method…………………………………………………….. 16

3.1 Passive Attenuator Design……………………………………….. 16

3.1.1 T- Attenuator…………………………………………………. 17

3.1.2 Pi Attenuator…………………………………………………. 18

3.2 Resistive Elements Models ……………………………………… 18

3.3 Buffer Amplifier………………………………………………….. 19

v

3.4 Resonator Network……………………………………………………. 20

3.4.1 Modeling the Resonator…………………………………………… 24

3.4.2 Coaxial Resonator Tuning………………………………………… 26

3.5 Varactor Diode Tuning………………………………………………… 26

3.5.1 Mathematical model of a Varactor………………………………… 28

3.5.2 Tuning Ratio of the Varicap……………………………………….. 29

3.5.3 Varactor in VCOs…………………………………………………… 29

3.6 Directional Coupler…………………………………………………….. 29

3.7 Bias Networks and Tees………………………………………………... 30

3.8 Shielding ………………………………………………………………. 31

Chapter 5 Process and Results…………………………………………….. 32

5.1 VCO’s Transistor Measurements……………………………………… 32

5.2 Attenuator Results……………………………………………………... 32

5.3 Buffer Amplifier…………………………………………………..…… 34

5.4 Power Supply Bias…………………………………………………….. 36

5.5 Coupler Design………………………………………………………… 38

5.6 Voltage Controlled Oscillator (VCO) Circuit………………………….. 41

5.7 Fabrications and Measurements ……………………………………….. 44

Chapter 6 Discussions & Conclusions……………………………………… 48

Chapter 7 Future Work……………………………………………………... 54

References……………………………………………………………………. 55

Appendices……………………………………………………………………. 57

vi

List of Figures

Page No

Fig. 1.1: Far Field shielding as a function of frequency for different materials…. 4

Fig. 1.2: DRO response with temperature control …………………………….. 6

Fig. 1.3: Temperature Performance of a 9 GHz DRO…………………………. 7

Fig. 1.4 The transistor oscillator ……………………………………………… 8

Fig. 1.5: Low Frequency current noise at 100 Hz and oscillator’s phase

noise at offset of 100Hz …………………………………………….. 9

Fig. 2.1: Reciprocal Mixing …………………………………………………… 13

Fig. 3.1: Tee attenuator …………………………………………………..…… 17

Fig. 3.2: Pi attenuator…………………………………………………………. 18

Fig. 3.3: Equivalent Circuit of a Resistor at high frequencies……………. …. 19

Fig. 3.4: Typical coaxial ceramic Resonator…………………………………. 21

Fig. 3.5: Equivalent circuit of a Coaxial Resonator………………………… .. 22

Fig. 3.6: Self Resonant Frequency of Coaxial Resonator………………… …. 23

Fig. 3.7: Parallel RLC Model for the Resonator……………………………… 24

Fig. 3.8: Impedance Response of the resonator model……………………….. 25

Fig. 3.9: Equivalent Model of the coaxial resonator with pads………………. 25

Fig. 3.10: Impedance vs. Frequency response for the model with pads……… 26

Fig. 3.11: Varactor Diode Equivalent Model…………………………………. 27

Fig. 3.12: Junction Capacitance as a function of Bias Voltage + Contact Potential 27

Fig. 3.13: Equivalent Model for a varactor…………………………………… 28

Fig. 3.14: Coupled lines Directional coupler…………………………………. 30

Fig. 4.1: VCO’s transistor measurements…………………………………….. 32

Fig. 4.2: Schematics of the 10 dB Pi Attenuator……………………………… 33

Fig. 4.3: S parameter simulations of the 10 dB attenuator……………………. 33

Fig. 4.4: Input and Output Impedance of the Attenuator……………………… 34

Fig. 4.5: Buffer Amplifier Schematics with 3V, 21mA bias point……………. 35

Fig. 4.6: Response of the Buffer amplifier……………………………………. 35

Fig. 4.7: Input and output impedance match of the buffer amplifier………….. 36

Fig. 4.8: Schematics of a bias Tee…………………………………………….. 37

Fig. 4.9: Layout of the bias Tee……………………………………………….. 37

Fig. 4.10: Simulations results of the Bias Tee………………………………… 38

Fig. 4.11: Schematics of 12 dB Coupler………………………………. …….. 39

vii

Fig. 4.12: Response of the 12 dB Coupler……………………………………. 40

Fig. 4.13: Schematics of the Voltage Controlled Oscillator …………………. 41

Fig. 4.14: Layout of the Voltage Controlled Oscillator………………………. 41

Fig. 4.15: OscTest Response of the Oscillator………………………………... 42

Fig. 4.16: PCB of the VCO…………………………………………................ 44

Fig. 4.17: VCO measurements through Spectrum Analyzer…………………. 45

Fig.4.18: Load Pull measurements …………………………………………... 47

Fig. 5.1: Schematics for Matching Network of the Buffer Amplifier………... 49

Fig. 5.2: Results of the Matching Network of Buffer Amplifier……………... 50

Fig. 5.3: Recommended pad for the Resonator………………………………. 50

Fig. 5.4: Resonator with Pads, One Port Test circuit………………………… 51

Fig. 5.5: One Port Measurements of the Resonator………………………….. 51

viii

List of Tables

Page No

Table 1.1: Phase Locked DRO/CRO Performance ………………………………… 2

Table 1.2: Properties of Shielding Materials …………………………………….. 3

Table 2.1: Center Frequency, Tuning range (absolute and relative)

for different standards ……………………………………………….. 14

Table 4.1: Oscillation Frequency of VCO as a function of varactor bias voltage … 43

Table 4.2: Results of the VCO for the Varactor tuning………………………….. 45

Table 4.3: Results of the VCO over a Temperature Range……………………… 46

Table 5.1: Tuning range results with varying capacitor values………………….. 48

1

Chapter 1 Introduction

1.1 Introduction

This Masters Degree Project is a study, design and implementation of a C band

microwave oscillator for the C band transceiver, used in wave radar. The most

important parameters affecting the microwave oscillator design are studied which

include the tuning range, shielding of the oscillator circuits, temperature performance

and frequency instability due to load and supply pulling.

A state of the art phase locked DRO/CRO is described, mainly used in space

applications [1]. Previously the implementation of oscillators was realized using

crystal oscillator followed by a chain of multipliers for good stability and phase noise.

The new approach is to use a Dielectric Resonator Oscillator (DRO) or a Coaxial

Resonator Oscillator (CRO). This approach provides very good long term stability,

better temperature performance and reduced sizes. The DRO or CRO is phase locked

to a temperature compensated crystal oscillator (TCXO). The main advantage of the

phase locked loop is that the crystal oscillator’s long term stability is inherited to the

DRO or CRO. The offset frequencies within the loop have the same phase noise and

bandwidth as that of the crystal oscillator. This eliminates the use of filters for

removing spurious harmonics. The resonators used, are made of dielectric materials.

These have a very high unloaded Q at microwave frequencies and are insensitive to

radiations which make them ideal for aerospace applications. The tuning of these

resonators is very simple as well. Overall the entire phase locked loop DROs and

CROs have shown good spurious and phase noise performance and are less

complicated. Table 1 shows some of the characteristic results of the B. Hitch and T.

Holden’s DRO and CRO implementations.

2

𝑷𝒆𝒓𝒇𝒐𝒓𝒎𝒂𝒏𝒄𝒆 𝑷𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓 𝑷𝒉𝒂𝒔𝒆 𝑳𝒐𝒄𝒌𝒆𝒅 𝑪𝑹𝑶 𝑷𝒉𝒂𝒔𝒆 𝑳𝒐𝒄𝒌𝒆𝒅 𝑫𝑹𝑶

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑆𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ± 1.5 𝑝𝑝𝑚 𝑎𝑙𝑙 𝑐𝑎𝑢𝑠𝑒𝑠 ± 1.5 𝑝𝑝𝑚 𝑎𝑙𝑙 𝑐𝑎𝑢𝑠𝑒𝑠

𝑃𝑕𝑎𝑠𝑒 𝑁𝑜𝑖𝑠𝑒

10 𝐻𝑧 −63 𝑑𝐵𝑐/𝐻𝑧 −63 𝑑𝐵𝑐/𝐻𝑧

100 𝐻𝑧 −94 𝑑𝐵𝑐/𝐻𝑧 −94 𝑑𝐵𝑐/𝐻𝑧

1 𝐾𝐻𝑧 −113 𝑑𝐵𝑐/𝐻𝑧 −113 𝑑𝐵𝑐/𝐻𝑧

10 𝐾𝐻𝑧 −117 𝑑𝐵𝑐/𝐻𝑧 −117 𝑑𝐵𝑐/𝐻𝑧

100 𝐾𝐻𝑧 −120 𝑑𝐵𝑐/𝐻𝑧 −128 𝑑𝐵𝑐/𝐻𝑧

Table 1.1: Phase Locked DRO and CRO performance [1]

The stability of signal source depends on maintaining the phase locked loop

conditions. The bandwidth requirements may force to use multiple narrowband

ceramic CROs. The spectral purity of these ceramic CROs is very good but they have

several disadvantages. These include limited temperature and tuning ranges. Another

disadvantage is that they are not suitable for integrated circuits (ICs) fabrication at the

present. Further more the ceramic resonators are sensitive to phase hits due to tension

in the crystal structure [2].

1.2 Susceptibility to Electromagnetic Fields and Shielding

Electronic circuits may be classified as shielding circuits, non-shielding circuits and

semi-shielding circuits each having different requirements for shielding in a

multilayer PCB. The three-dimensional configuration of the shielding circuits plays a

vital role in achieving a stable shielded structure [3]. The shielding may be electric,

magnetic or electromagnetic in nature.

The electromagnetic shield takes the form of an enclosure which consists of metal

plates and foils usually. The electromagnetic shield construction on the actual printed

board also determines its effectiveness. The two factors which increase the efficiency

of the electromagnetic shields are the electrical contact in the shield layer and making

the path longer for the leakage of the electromagnetic fields. This increases the

efficiency of the contact joints in electromagnetic shields [4].

3

The aerospace structures require a high degree of electromagnetic interference (EMI)

shielding, compared to other electronics structures. The weight of these shields is a

limiting factor, thus a high strength, high elastic modulus and light weight shields are

required with better EMI shielding abilities. Metallic shields are used currently which

have higher densities.

𝑴𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝑫𝒆𝒏𝒔𝒊𝒕𝒚

𝒈/𝒄𝒎𝟑

𝑹𝒆𝒔𝒊𝒔𝒕𝒊𝒗𝒊𝒕𝒚

𝝁𝛀 𝒄𝒎

𝑺𝒕𝒓𝒆𝒏𝒈𝒕𝒉

𝑴𝑷𝒂

𝑴𝒐𝒅𝒖𝒍𝒖𝒔

𝑮𝑷𝒂

Copper 8.96 1.78 420 110

Iron 7.86 10 200 200

Aluminum Alloy 2.80 10 520 71

Aluminum 2.70 2.82 210 60

Beryllium 1.85 4.0 620 290

P-100 + Br/epoxy 1.78 90 840 430

P-100/epoxy 1.72 460 840 430

T-300/epoxy 1.51 5000 3200 228

Table 1.2: Properties of shielding materials [5]

Table 1.2 describes some of the properties of the metallic and composite shielding

materials. The most commonly used and most effective shielding material is

aluminum, but it has a very high density. Carbon fibers are light weight, but not

having enough conductivity, which results in insufficient shielding. Paints, plating

and foils on the carbon composites may provide needed shielding, but there are issues

with reliability, scratching, low adhesion and they may oxidize in air.

The Fig. 1.1 describes the total far field shielding at different frequencies for different

materials. At low frequencies the attenuation is almost frequency independent, until

up to some characteristic value after which it increases sharply. The metals Cu and Al

provide the best shielding as the attenuation rises sharply after 105 Hz. The other

composites have low shielding at high frequencies, PAN having the least.

4

Fig. 1.1: Far Field shielding as a function of frequency for different materials [5]

The Al/Cu foil is very effective EMI shield. It is low cost and may be used with high

conductive adhesive. The EMI conductive coatings or adhesives on light weight

plastics is also becoming in use. These conductive paints are of many types such as

silver-copper paints, copper, nickel or silver paints etc [6].

The phase cancellation principle works in uniform magnetic materials at front face

providing up to 40 dB absorption per ounce. For 50-800 MHz frequency range, spinal

ferrites are used while for 800 MHz-2 GHz frequencies, ferroxplana is common. On

the contrary thick EMI shielding materials with a uniform dielectric does not follow

the phase cancellation principle due to their lossy conductor fibers where the

absorption is equivalent to the power loss. These have low densities and

permittivities. Comparing with ferrites, metals have higher permittivities at

microwave frequencies and are better EMI absorbers. The losses of the magnetic

absorbers are dependant on their magnetic fields so a non-conducting material is

desired. Dielectric absorbers require thick layers, where the relative permittivity is

desired close to one. Practically these absorbers have higher permittivities, so are not

appropriate in many cases [7].

5

Another problem in circuits is the low frequency Electromagnetic Pulse (EMP).

Filtering this EMP is usually achieved through proper isolation which is provided by

highly permeable ferrite shields. But in cases where there are large distances between

the wave impedance of the shield and the intrinsic impedance of the metal, a higher

reflection occurs for the impinging wave. Thus copper and aluminum are preferred

choices compared with ferrites in such conditions. It can be concluded that with low

frequencies and large separation between source of the signal and the shields, higher

conducting materials provides better shielding abilities [8].

1.3 Tuning Range

The tuning network plays a key role in defining the frequency range of an oscillator.

The tuning network consists mainly of the resonator whose type determines the

frequency of oscillation. The voltage controlled oscillator may have frequency output

at some specified frequency range. In general, higher the center frequency of the

oscillator, the more difficult the design is. Oscillators are analyzed usually over a

frequency range around the center frequency.

The MMIC varactor diode has a specific tuning range provided by the manufacturer.

The introduction of negative resistance connected to the varactor diode using an

active circuit increases the varactor’s tuning range more than 10 times. In wide band

VCOs, the frequency range relation 𝑓𝑚𝑎𝑥

𝑓𝑚𝑖𝑛 is proportional to the tuning range of the

varactor diode 𝐶𝑚𝑎𝑥

𝐶𝑚𝑖𝑛 . The negative capacitance can be created by two common

source transistors loaded with inductor [9].

1.4 Temperature Performance

The temperature variations affect the performance of the active devices and oscillator

as a whole. For oscillators, a working temperature range is defined and the change in

the output power of the oscillator is specified in that temperature range. The

simulations usually imply that the junction temperature is constant at 25𝑜𝐶. For this

oscillator design, a range of 0𝑜 − 60𝑜 C is specified.

6

The temperature variations also affect the operation of the oscillators causing a

change in the output power and frequency. The temperature stability is improved by

having a temperature controlled resonator in a DRO based on simple loop design. The

dynamic temperature sensitivity depends on the ambient temperature variations. The

copper may expand and contract relative to ambient temperature quicker than the

dielectric puck which has a poor thermal conductivity. The static temperature

conductivity describes the equilibrium between the initial and final ambient

temperatures and is a function of temperature coefficients, thermal expansion of the

dielectric material and cavity. A temperature control circuit is used consisting of a

resistive heater mat, and NTC thermister to sense the temperature [10]. The Fig. 1.2

describes the temperature sensitivity of the 1.3 GHz DRO. The temperature control

enabled is represented by the red line and show a stable frequency offset with

temperature while the temperature disabled control show large variations in frequency

offset.

Fig. 1.2: DRO response with temperature control [10]

Fig. 1.3 shows the temperature response of a 9 GHz DRO, with a CW output power of

2.5 watts at room temperature using high power GaAs MESFET. The frequency

stability is 130 𝑝𝑝𝑚 without any temperature compensation from −50𝑜𝐶 𝑡𝑜 +

+50𝑜 𝐶. The variation in output power at −50𝑜 𝐶 is +35 𝑑𝐵𝑚 (3.2 𝑊) and at

+50𝑜 𝐶 was 33 𝑑𝐵𝑚 (2 𝑊) which describes output power as a function of the

temperature [11].

7

Fig. 1.3: Temperature performance of a 9 GHz DRO [11]

1.5 Frequency Pulling due to Load

The load variations affect the frequency of the voltage controlled oscillator (VCO).

The variation in the output impedance affects the DC voltages of the VCO’s

transistor. The BJT (Bipolar Junction Transistor) has supply voltages for different

junctions that must be constant throughout the operation of the oscillator. A change in

the Base-Collector voltage (𝑉𝐶𝐵) is caused by the change in the VCO’s output Base-

Collector capacitance. This varies the frequency of oscillation to a large value. Load

pulling is minimized by using a very high isolation stage between the load and VCO.

Frequency Pulling is a measure of the shift in frequency for a unity VSWR load

(usually 50 ohms) to the non-unity VSWR due to change in the load.

The load pulling measurements are done using variable transmission line and a load

impedance which is not matched. The VCO and load are connected together. The

transmission line is used for varying the phase angle between the load and VCO

between 0𝑜 − 360𝑜 . In this way the frequency variations due to the load variations

are measured.

8

A very linear MIC bipolar VCO with 100 MHz FM rate is described where the

frequency pulling is ± 1 𝑀𝐻𝑧 into a 2:1 mismatched load. The power flatness and

immunity from load pulling is achieved by using a two stage GaAs FET buffer

amplifier. The total load isolation achieved is more than 45 dB. The FET amplifier

provides 35 dB of isolation while 12 dB of isolation is provided by a thin film pi

attenuator [12].

1.6 Frequency Pulling due to Supply

The frequency of the VCO is affected by the supply voltage to some extent. In

transceiver systems, power amplifier uses a lot of the power and turning it on, will

increase the current drastically, which may affect the LO power supply and the VCO

frequency will increase. This can be minimized by isolating the VCO unit from the

power amplifier unit. The battery supply voltage drops to a certain minimum during

its life time and the oscillator design should work in a certain range of voltage. This

may be indicated in terms of tolerance as well for example ±10 % of 3 𝑉 power

supply. Temperature also affects the supply voltage bias. Noise on the supply voltage

lines causes noise and spurious on the oscillator.

The external environmental conditions like temperature or supply voltage variations

affect the active elements of the microwave oscillators thus inducing frequency

instability. The two reasons for this instability are variations in the cut off frequency

and collector capacitance. For the analysis, a simple tuned circuit is chosen as a

passive frequency determining network while a common base configuration is

selected for the active element as seen in Fig. 1.4.

Fig. 1.4 The transistor oscillator [13]

9

The high frequency analysis shows that the two most important parameters of the

reactive elements of the transistor are the collector capacitance and the frequency

dependence of the current gain. Variations in these factors give rise to variations in

the oscillation frequency. The collector capacitance is mainly a function of the

collector voltage. The relation between the changes in collector capacitance 𝐶𝑐 and

Collector voltage 𝑉𝑐 for a typical p-n-p transistor is given in eq. 1.1.

𝜕 𝐶𝑐

𝐶𝑐= −

1

2 𝜕 𝑉𝑐

𝑉𝑐 (1.1)

The effective base width of the transistor depends on the collector voltage and hence

frequency of oscillation. The Ebers and Miller [14] equation for the relation between

the 𝑓𝑎 and 𝑉𝑐 is approximated as

𝑓𝑎

𝑓𝑎𝑜 = 1 + 𝐾𝑉𝐶 𝑓𝑎𝑜 (1.2)

where

𝑓𝑎𝑜 = 𝑇𝑕𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓𝑎𝑓𝑜𝑟 𝑧𝑒𝑟𝑜 𝑉𝑐

The low frequency (LF) noise up conversion in HBT transistors significantly

contributes to the close in carrier phase noise of the transistor based microwave

oscillators [15]. High Q resonator networks are used with HBT transistors having LF

noise, to reduce close in carrier phase noise. The noise up conversion factor is

adjusted to reduce further this close in carrier noise. The investigations showed that

there was a 15 dB reduction in phase noise by maintaining the bias point where the

small transistor phase sensitivity is observed to the transistor bias current.

Fig. 1.5: Low Frequency current noise at 100 Hz and oscillator’s phase noise at

offset of 100 Hz [15].

10

The Fig. 1.5 shows the measured and predicted results and are calculated based on

curve fitted LF noise. The experimental results predicts that the residual phase noise

of the HBT based oscillators is a function of the bias dependant LF noise up

conversion factor of the device. This concludes that for a low phase noise, the two

important decisions are device selection and matching network design.

The variations in supply voltage could cause a change in the output power of the

microwave oscillator. The output power can be controlled for microwave oscillators

by varying the bias voltage of the active element while using the scheme with a

synchronized oscillator. The results from the theoretical and experimental

investigations proves that a change of 0.2 V or 2.7 % of bias voltage change may

cause an output power change of up to 40 dB, with frequency being the constant

factor [16].

1.7 Thesis Outline

Chapter 2 describes the theory of the oscillator design. The different types of

oscillator topologies are described. There is a discussion of the oscillator properties,

characteristics and limitations.

Chapter 3 describes the design strategies of the VCO and the sub circuits used in it.

These sub circuits include the attenuator, buffer amplifier, resonator, and varactor

tuning network, coupler etc.

Chapter 4 consists of the simulations, results and fabrication of the VCO. The

expected results are analyzed to the measured results.

Chapter 5 describes the conclusions, discussions, week points and probable solutions

to these problems. It also includes a comparative study of this project results with the

state of the art work done by the others.

Chapter 6 gives an idea of the future work to be done in this design.

11

Chapter 2 Theory

2.1 Theory of Oscillators

An oscillator is a non linear circuit which transforms DC power to an AC waveform.

This circuit usually consists of an amplifier, a resonator and a feedback network. The

feedback may be internal i.e. a part of energy from the active device is fed back to the

resonator or it may be an external feedback circuit.

The active device in the oscillator takes in DC power from a regulated supply and for

an input power gives a specific output power which is several times higher in

magnitude. It can be a bipolar junction transistor (BJT), or a field effect transistor

(FET) or a Gain block which is usually wideband.

The specifications affecting the quality of operation of the whole system depends on

the cleanliness of the oscillator signal i.e. low phase noise and low spurious, which

constitute noise in systems. The desired characteristics for oscillators are sufficient

output RF power level, low phase noise, efficiency and stability of the signal etc.

Several noises contribute to the total noise of the oscillator. These include losses in

the resonator, transistor noise, noises modulated in power supply and noise due to the

varactor diode tuning.

2.2 Microwave Oscillator Configurations

There are three types of approaches for designing oscillators.

In one port oscillators, the transistor and the feedback network is replaced by a

negative resistance. For example, in Colpitt and Clapp oscillators, the capacitive

feedback creates a negative resistance along the tuning network.

In two port oscillators, the transistor acts as a two port device with its third terminal

grounded. The tuning network is used for the feedback which determines the

frequency. Such oscillators have a specific gain, phase shift, resonator network and

matching network.

12

Three port oscillators have an inductor at the base with some capacitance at the output

port. This feedback configuration generates negative resistance at input and output

port.

2.3 Voltage Controlled Oscillators

Voltage controlled oscillators or simply VCOs are the class of oscillators in which the

frequency determining reactance is varied by voltage. For high frequency

applications, the voltage controlled element is a typical varactor diode.

The VCOs find its use in many important applications such as function generators,

transmitters of every kind, frequency synthesizers and almost every type of wireless

communication equipment.

2.4 Considerations in Oscillators

2.4.1 Phase Noise

Phase noise is measured as dBc in a bandwidth of 1 Hz at an offset of a specific

frequency. There are several types of noises and spurious which modulate the output

signal of the VCO on either sides of the carrier.

Phase noise is short term phenomenon and some of the possible causes of phase noise

due to improper isolation are

Variations in the impedance of load

Mismatch reflections back to the VCO’s output

Rise in ground current

Coupling of radiations from nearby layout circuits

Changes in the bias supply of the VCO transistor due to load variations

The loaded Q is mainly responsible for the phase noise performance [17].

2.4.2 Harmonic Suppression

The typical harmonic suppression of a voltage controlled oscillator is about 15 dB, but

for certain systems, a very low harmonic content is desired. This can be achieved by

placing a microstrip low pass filter at the output.

13

2.4.3 Spurious signals in the Oscillator Output

Apart from harmonics, unwanted signals found on the sides of the carrier of an

oscillator are called spurious. A spurious free range is usually specified in terms of

dB. The synthesizer signals may be a cause for the generation of these spurious.

2.4.4 Post-tuning Drift

The tuning network which is a varactor diode is biased with supply voltage. After the

supply voltage has been applied, the frequency of the oscillator still drifts for some

time. This drift can affect the voltage controlled oscillators tuning speed.

2.4.5 Blocking or Reciprocal Mixing

The mixing of the local oscillator noise sidebands with the incoming strong signals is

called reciprocal mixing or blocking. This mixing produces unwanted noise at the

intermediate frequency. Fig. 2.1 shows the carrier signal A´ of the oscillator mixes

with the wanted signal A. The side bands of the oscillator B´, C´, D´ mixes with the

undesired signals A, B, C and creates interference in the intermediate frequency IF.

This affects considerably the receiver selectivity of increasing the noise floor.

Fig. 2.1 Reciprocal Mixing [18]

14

2.4.6 Linear Tuning characteristics

A linear relationship is desired for the variations in the frequency of the oscillator,

caused by varying the tuning voltage. This is an important factor for the stability of

synthesizers. Table 2.1 shows some standards for wireless communications. The

center frequency and tuning range (absolute and relative) is given for each standard.

The absolute tuning range shows the minimum and maximum frequencies while

relative tuning describes the percentage of the center frequency. The relative tuning

ranges for TV receiver, Satellite TV front end and DVB-T and FM radio front end are

very high. The GSM and UMTS relative ranges are narrow band with just around 3%.

The SONET standards are for fixed bit rates and only the center frequency is

indicated.

Table 2.1 Center Frequency, Tuning range (absolute and relative) for

different Standards [19]

The oscillator design requires a tuning range of about 80-100 MHz around the center

frequency.

2.5 Choice of the Active Device and Modeling

The two main choices available are FET and bipolar transistors. The transition

frequency and flicker noise corner frequency are important while choosing the active

device for the oscillator.

15

The frequency of transition 𝑓𝑇 of a transistor plays an important role in defining its

frequency of oscillation. The bipolar transistors have a 𝑓𝑇 of up to 25 GHz where as

SiGe based transistors have higher values of 𝑓𝑇 upto 100 GHz. The improved GaAs

based bipolar transistors called Heterojunction bipolar transistors (HBTs) have 𝑓𝑇 of

about 100 GHz also but it costs much more than silicon based transistors.

The flicker noise frequency of HBTs is higher than the SiGe transistors but it is not

prominent in practical circuits which have high lossy transmission media. Thus the

total oscillator noise in SiGe transistors and HBTs remains almost the same.

2.6 Loaded Q

The Loaded Quality factor of an oscillator is

𝑄𝐿 = 2𝜋 𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑 𝑖𝑛 𝑡𝑕𝑒 𝑠𝑦𝑠𝑡𝑒𝑚(𝑖𝑛 𝑜𝑛𝑒 𝑓𝑢𝑙𝑙 𝑐𝑦𝑐𝑙𝑒)

𝐸𝑛𝑒𝑟𝑔𝑦 𝑙𝑜𝑠𝑡 𝑖𝑛 𝑡𝑕𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑖𝑛 𝑒𝑎𝑐𝑕 𝑐𝑦𝑐𝑙𝑒

In steady state, the external source supplies the energy to be lost.

The high loaded Q has certain advantages.

The high loaded Q reduces the frequency drift as resonator becomes the sole

frequency determining component.

The isolation of the resonator from the active device reactance minimizes the

effect of temperature.

The long term stability and phase noise performance is improved.

16

Chapter 3 Method

3.1 Passive Attenuator Design

Attenuator is a circuit which reduces the power of an incoming signal without the

significant distortion of the signal waveform and attenuation is expressed in 𝑑𝐵. The

main purpose of the attenuator, in combination with a buffer amplifier, is that the

proper output signal level is maintained at the VCO’s output and thus valuable reverse

isolation is achieved.

The VSWR values are of critical importance in the design of attenuators with resistive

elements. The attenuator is also used to improve the input match of the amplifier. This

may decrease the VSWR ratio at the input of the buffer amplifier and improve gain.

On the other side, every dB of attenuation at the input of the buffer amplifier increases

the Noise Figure (NF) of the amplifier.

The desirable characteristics of attenuators are reliability at the frequency of operation

and power applied to it. The attenuator design is usually achieved with the help of

resistors. The resistors used are usually surface mount. Since the output power from

the VCO transistor is few milliwatts, thus it doesn’t affect the device performance a

lot due to heating considerations.

Low Standing Wave Ratio (SWR) at input and output of the attenuator is always

desired. The low SWR at input and output can be achieved by careful design of the

attenuator circuit usually by having a symmetrical network. The SWR of the

attenuator and the input and output networks will contribute to the mismatch. This

variation is frequency dependant and it may degrade the flatness response of the

attenuator. The SWR at the input of attenuator may not be very important as VCO

transistor’s output is loaded with the attenuator to maintain the negative resistance

region. But at the output, a stable SWR is required to have the required reverse

isolation and matching. [20]

There are several topologies for achieving the attenuation in circuits. The passive

techniques i.e. Tee and Pi configurations are described here.

17

3.1.1 Tee Attenuator

Fig. 3.1 shows the Tee attenuator configuration and consists of two resistors of the

same value which are the series R1 & R2 resistors.

Z in Z out

R 1 R 2

R 3

Fig. 3.1: Tee attenuator

The resistances R1, R2 and R3 are calculated as

𝑅3 = 1

2 10

𝐿

10 − 1

𝑍𝐼𝑁 𝑍𝑂𝑈𝑇

10 𝐿

10

(3.1)

𝑅2 = 1

10 𝐿

10

+ 1

𝑍𝑂𝑈𝑇 (10 𝐿

10 − 1)

− 1𝑅3

(3.2)

𝑅1 = 1

10 𝐿

10

+ 1

𝑍𝐼𝑁 (10 𝐿

10 − 1)

− 1𝑅3

(3.3)

where

L = desired attenuation expressed in dB

𝒁𝑰𝑵 = desired Input impedance expressed in ohms

𝒁𝑶𝑼𝑻 = desired Output impedance expressed in ohms

18

3.1.2 Pi Attenuator

Fig. 3.2 shows the Pi attenuator configuration consisting of two resistors of the same

value i.e. R1and R2.

Z in Z out

R 1 R 2

R 3

Fig. 3.2: Pi attenuator

The resistances R1, R2 and R3 are calculated as

𝑅3 = 2 𝑍𝐼𝑁 𝑍𝑂𝑈𝑇 10

𝐿

10

10 𝐿

10 − 1

(3.4)

𝑅2 = 10

𝐿

10

+ 1

10 𝐿

10 − 1

𝑍𝑂𝑈𝑇 − 𝑅3 (3.5)

𝑅2 = 10

𝐿

10

+ 1

10 𝐿

10 − 1

𝑍𝐼𝑁 − 𝑅3 (3.6)

In terms of transducer gain which is equal to the attenuation of the attenuator

𝐴𝑡𝑡𝑒𝑛𝑢𝑎𝑡𝑖𝑜𝑛 = 𝑆21 2

3.2 Resistive Elements Models

The attenuator at low frequency can be designed using simple formulas as the

resistors act as lumped components. The resisters at high frequency have different

behavior at different frequencies and depend on a number of processes like the type of

resistors selected, accurate models for those resistors, accurate pads etc.

19

The factors affecting the modeling of the resistors at high frequencies are [21]

Dimensions of the resistor (Length, width, height etc.)

Skin Effect

Ground plan layout

The electrical length of the resistor relative to quarter wavelength

(approximately 1/10)

Components at high frequencies behave as non-ideal. For example the capacitor leads

have significant inductance while inductors have some self-capacitance. The Q of the

inductors is also considerable along with the parasitics due to coupling between

inductors. These parasitics should be considered in design and simulations. There are

parasitics associated with amplifiers as well. Thus the real world resistor acts as a

distributed component at high frequencies. Proper modeling of the resistors and other

components make them behave as lumped even at very high frequencies.

Fig. 3.3 shows the equivalent circuit of a resistor at high frequency, with a parasitic

inductance 𝐿𝑆 in series and parallel capacitance 𝐶𝑃. The parasitic reactance is

dependant upon the dimensions and mounting techniques of the resistors. The

inductance is usually just a few 𝑛𝐻 while the capacitance is a fraction of a pF.

Fig. 3.3 Equivalent Circuit of a Resistor at high frequencies

3.3 Buffer Amplifier

The component selected for providing the reverse isolation and amplification, in the

oscillator, is a low noise amplifier. It is Avago’s MGA-665P8 GaAs MMIC. It has a

unique active power down function. The features of this gain block are high gain, low

noise Figure and very high reverse isolation. It is incorporated in LPCC package

suitable for surface mounting. This improved performance is based on the Avago’s

20

state of the art E-HEMT (Enhancement Mode Pseudomorphic High Electron Mobility

Transistor).

There is a very good isolation between the output and input of the two stage MGA-

665P8 amplifier. It has a very low 𝑆22 i.e. −21.83 𝑑𝐵 while 𝑆12 is −37.72 𝑑𝐵, at 5.8

GHz. Thus there is a very good output match at the output. At the input, 𝑆21 is

15.99 𝑑𝐵 while 𝑆11 is −5.5 𝑑𝐵, at 5.8 GHz. Since the gain of the amplifier is very

high and a very high reverse isolation is present, thus no impedance matching is used

in the design. The buffer amplifier consists of two stages of amplifiers, each requiring

a separate bias. The pin 6 is supplied directly with the bias while the pin 7 is supplied

with a bias fed through a Bias Tee.

3.4 Resonator Network

The frequency of resonance determines the type of resonator used. For low

frequencies, lumped resonators are used while at higher frequencies, coaxial, ceramic,

microstrip resonators are commonly used. It also determines the phase noise

performance of the oscillator.

Fig. 3.4 shows a ceramic resonator with outer square cross section and inner

cylindrical shape. The W and 𝑙 are the width and length of the outer conductor while d

is the inner conductor diameter.

The approximate characteristic impedance of the coaxial line resonator is

𝑍𝑜 = 60

휀𝑟ln 1.08

𝑊

𝑑 (3.7)

The 𝑅𝑜 is usually between 5- 15 ohms while 휀𝑟 is from 10 to 100. This reduces the

size of the length of these resonators and is suitable for many applications including

spacecrafts.

𝜆𝑒𝑓𝑓 = 𝜆𝑓𝑟𝑒𝑒

휀𝑟 (3.8)

21

Fig. 3.4 Typical coaxial ceramic Resonator [22]

The calculation of length of the quarter wave shorted coaxial resonator length is

𝑅𝑒𝑠𝑜𝑛𝑎𝑡𝑜𝑟 𝐿𝑒𝑛𝑔𝑡𝑕 = 1

4 𝜆𝑐𝑜𝑎𝑥 (3.9)

The unloaded Q factor of the coaxial resonator is

1

𝑄𝑈=

1

𝑄𝐶+

1

𝑄𝐷 (3.10)

where

𝑄𝐶 = 𝑄 𝑑𝑢𝑒 𝑡𝑜 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝐿𝑜𝑠𝑠𝑒𝑠

𝑄𝐷 = 𝑄 𝑑𝑢𝑒 𝑡𝑜 𝐷𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝐿𝑜𝑠𝑠𝑒𝑠

The 𝑄𝐶 is due to the conductor current flow and is given as

𝑄𝐶 =2 𝜋 𝑓 𝜇𝜍

1𝑎 +

1𝑏

ln𝑏

𝑎 (3.11)

where

𝜇 = 𝑃𝑒𝑟𝑚𝑒𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑛𝑑𝑢𝑡𝑜𝑟

𝜍 = 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑛𝑑𝑢𝑡𝑜𝑟

The 𝑄𝐷 is due to the dielectric material that is in between the two conductors lines a

and b in the coaxial resonator.

𝑄𝐷 = tan 𝛿 = 𝜍

2 𝜋 𝑓 휀1휀𝑟 (3.12)

where

22

𝜍 =1

𝜌= 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡𝑕𝑒 𝐷𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐

휀𝑟 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑃𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦

휀𝑜 = 𝑃𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡𝑕𝑒 𝑓𝑟𝑒𝑒 𝑠𝑝𝑎𝑐𝑒 = 8.854 × 10−12 𝐹 𝑚−1

A cylindrical coaxial resonator with inner conductor diameter d and outer conductor

diameter W. The equivalent circuit of this coaxial resonator is a parallel RLC circuit

as given in Fig. 3.5. The coaxial resonator is plated with silver plating.

R C L

Fig. 3.5 Equivalent circuit of a Coaxial Resonator

The unloaded Q for this coaxial resonator is

𝑄𝑈 = 𝑘 𝑓𝑜 ln(1.079

𝑊𝑑

)

25.4(1𝑊 +

1𝑑

) (3.13)

where

𝑊 = 𝑂𝑢𝑡𝑒𝑟 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑑 = 𝐼𝑛𝑛𝑒𝑟 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑘 = 240 𝑓𝑜𝑟 𝑠𝑖𝑙𝑣𝑒𝑟𝑒𝑑 𝑑𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑤𝑖𝑡𝑕 휀𝑟 = 38.6

𝑘 = 200 𝑓𝑜𝑟 𝑠𝑖𝑙𝑣𝑒𝑟𝑒𝑑 𝑑𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑤𝑖𝑡𝑕 휀𝑟 = 88.5

The input impedance of the resonator is

𝑍𝐼𝑁 = 60

휀𝑟ln 1.079

𝑊

𝑑 (3.14)

The inductance L is

𝐿 = 𝑙 𝑍𝑜 8 휀𝑟

25.4 𝜋2 3 × 108 (3.15)

where

𝑙 = 𝑝𝑕𝑦𝑠𝑖𝑐𝑎𝑙 𝑙𝑒𝑛𝑔𝑡𝑕 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑎𝑥𝑖𝑎𝑙 𝑟𝑒𝑠𝑜𝑛𝑎𝑡𝑜𝑟 𝑖𝑛 𝑚𝑚

23

The Capacitance is

𝐶 = 𝑙 휀𝑟

25.4 × 2 × 3 × 108 𝑍𝑜 (3.16)

The resistance is

𝑅 =4 𝑍𝑜𝑄

𝜋 (3.17)

The characteristics of coaxial line resonators below resonance are, they are high Q

components and temperature stable and act as ideal inductor elements over a narrow

range of frequencies as seen in Figure 3.6. The coaxial resonator acts as a distributed

structure having capacitance and inductance. The line has a specific frequency at

which it resonate called Self Resonant Frequency (SRF). The line exhibits inductive

reactance when it is operated below the SRF while acts as capacitive if operated

above SRF.

Fig. 3.6 Self Resonant Frequency of Coaxial Resonator [23]

Compared to traditional coil resonators, the ceramic coaxial resonators have a number

of advantages

Their ruggedness makes it suitable for incorporating in PCBs.

They have a very good Q value

They have a better temparture stability perforamce

Immunity to microphonics

24

3.4.1 Modeling the Resonator

The CAD (Computer Aided Design) software used is Agilent ADS (Advanced Design

System). Since the manufacturer didn’t provide a specific CAD model for the

resonator, a model is established for this simulation purposes.

The quarter wave shorted coaxial resonator model can be realized by using the

parallel RLC circuit as below. The R, L and C values supplied by the manufacturer

are simulated in parallel RLC circuit as in Fig. 3.7.

Fig. 3.7 Parallel RLC Model for the Resonator

Fig. 3.8 shows the impedance response of the above model and it shows that the

impedance is highest at the 6.2 GHz frequency which is the frequency of oscillation.

Thus this model acts as specifications.

25

Fig. 3.8 Impedance Response of the resonator model

The manufacturer has its own recommended layout for the resonator pads as given in

Appendix B. The recommendations are followed and pads are added to the model as

shown in Fig. 3.9.

Fig. 3.9 Equivalent Model of the coaxial resonator with pads

This effectively changes the model supplied by the manufacturer. Fig. 3.10 shows that

the frequency is shifted and the new model oscillates at 5.137 GHz which is more

than one GHz below the frequency of the original model.

5.9 6.0 6.1 6.2 6.3 6.4 6.55.8 6.6

5.0E3

1.0E4

1.5E4

2.0E4

2.5E4

0.0

3.0E4

freq, GHz

mag(M

eas1)

Readout

m1

m1freq=mag(Meas1)=25641.000

6.200GHz

26

Fig. 3.10 Impedance vs. Frequency response for the model with pads

3.4.2 Coaxial Resonator Tuning

The prototype test circuit requires tuning for test purposes. This is due to the fact that

the resonator is coupled with the stray capacitances in the vicinity which decreases the

resonant frequency (SRF). There are three common methods for varying the SRF of

the resonator in oscillator. These methods are mechanical in nature.

The SRF can be increased by removing the silver metallization from the resonator’s

open end. This can be done from the top and also the bottom of the resonator. This

can increase the SRF about 10-20 % without degrading the unloaded Q factor.

Similarly the SRF can be increased by removing the silver metallization from the

shorted end but with some degradation of the Q value. The change of the position of

the ground plane can also vary the SRF [24].

3.5 Varactor Diode Tuning

Varactor diode or Voltage variable capacitor or simply varicap is a type of diode

whose capacitance is a function of its applied voltage. The varactor diode which acts

as capacitor in the presence of a shorted quarter wave resonator and is used to vary the

operating frequency of the oscillator.

4.6 4.8 5.0 5.2 5.44.4 5.6

5.0E3

1.0E4

1.5E4

0.0

2.0E4

freq, GHz

mag(M

eas1)

Readout

m1

m1freq=mag(Meas1)=17048.076

5.137GHz

27

Fig. 3.11 Varactor Diode Equivalent Model

Fig. 3.11 shows the varactor diode which is reverse biased for proper operation. A

small capacitor is also used in series with the varactor. This capacitor helps in

increasing the tuning range of the varactor.

The varactors may be built from Silicon and Gallium Arsenide (GaAs). Si is

economical for large scale production while GaAs provides higher Q values suitable

for high frequency applications. The advances in material gradient doping have paved

the way for improved processes. The abrupt junction is formed by the uniform

doping and is commonly used method. This provides an inverse square root

relationship which is considered as non linear.

The hyper abrupt junction provides a linear response over the frequency range by

varying the control voltage. These are narrowband in nature for linear region and the

Q is reduced, which imply that it can be used in lower frequency applications.

Fig. 3.12 Junction Capacitance as a function of Bias Voltage + Contact

Potential [25].

28

Fig. 3.12 shows the relationship of the junction capacitance and bias voltage along

with contact potential. With increase the control voltage of the varactor diode, the

capacitance of the varactor diode decreases and this shifts the oscillator’s frequency.

𝐴𝑏𝑟𝑢𝑝𝑡 𝐽𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐶𝐽 𝑉𝑅 = 𝐴 = 𝐶𝑗𝑜

1 + 𝑉𝑅𝜙 𝛾 (3.18)

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝐿𝑖𝑛𝑒𝑎𝑟 𝐶𝐽 𝑉𝑅 = 𝐹 = 𝐶𝑗𝑜

1 + 𝑉𝑅 𝛾

(3.19)

𝐻𝑦𝑝𝑒𝑟 𝐴𝑏𝑟𝑢𝑝𝑡 𝐽𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐶𝐽 𝑉𝑅 = 𝐻 = 𝐶𝑗𝑜

1 + 𝑉𝑅𝜙

𝛾 (3.20)

where

𝛾 = 0.5 𝑓𝑜𝑟 𝑎𝑏𝑟𝑢𝑝𝑡 𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛

𝛾 > 0.5 𝑓𝑜𝑟 𝐻𝑦𝑝𝑒𝑟 𝑎𝑏𝑟𝑢𝑝𝑡 𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛

𝜙 = 𝐽𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐶𝑜𝑛𝑡𝑎𝑐𝑡 ′𝑠 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 = 0.7 𝑣 𝑓𝑜𝑟 𝑆𝑖 & 1.1 𝑣 𝑓𝑜𝑟 𝐺𝑎𝐴𝑠

𝐶𝑗𝑜 = 𝐷𝑖𝑜𝑑𝑒 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑧𝑒𝑟𝑜 𝑣𝑜𝑙𝑡𝑠 𝑏𝑖𝑎𝑠 𝑣𝑜𝑙𝑡𝑎𝑔𝑒

𝑉𝑅 = 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑟𝑒𝑣𝑒𝑟𝑠𝑒 𝑏𝑖𝑎𝑠 𝑣𝑜𝑙𝑡𝑎𝑔𝑒

3.5.1 Mathematical Model for a varactor

The mathematical model of a varactor diode is described in Fig. 3.13. The variable

capacitance of the junction is 𝐶𝐽(𝑉) at applied voltage, while 𝑅𝑆(𝑉) is the series

resistance of the varactor diode. The diode has some constant parasitic capacitance 𝐶𝑃

as well due to packaging, dimensions of the diode and wiring. A parasitic inductance

is 𝐿𝑝 also present. The varactor diode is supplied with reverse bias voltage which

changes its capacitance and series inductance. This in turn changes the frequency

and/or phase of the electrical network.

Fig. 3.13 Equivalent Model of a Varactor Diode

29

3.5.2 Tuning Ratio of the Varicap

The tuning ratio is defined as the ratio in the capacitance between two values of the

applied reverse bias voltage.

𝑇𝑢𝑛𝑖𝑛𝑔 𝑅𝑎𝑡𝑖𝑜 = 𝐶𝑗 (𝑉2)

𝐶𝑗 (𝑉1)= (

𝑉1 + 𝜙

𝑉2 + 𝜙)𝛾 (3.21)

where

𝐶𝑗 𝑉1 = 𝐽𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑉1

𝐶𝑗 𝑉2 = 𝐽𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑉2

Provided that

𝑉1 > 𝑉2

3.5.3 Varactor in VCOs

The varactors are mainly used in VCOs for frequency tuning. The desirable

characteristics of varactors are

Minimum series resistance so that it does not affect the resonator Q

factor.

Less noise as its noise is added to the over all VCO noise

The appropriate tuning range and 𝐶 − 𝑉 characteristics [22]

3.6 Directional Coupler

The single section microstrip coupled line Directional Coupler consist of two

microstrip transmission lines close together. Due to this close proximity, the

electromagnetic energy or power is coupled between the lines.

Fig. 3.14 shows a microstrip directional coupler with four ports i.e. Input, transmitted,

coupled and isolated. One of the lines is termed as the “main line” which is between

port 1 and 2. This is the transmitted part where most of the power flows. The other

arm is called the coupled arm where a fraction of the input power is coupled. The

isolated port is terminated with matched impedance. The need for a coupler is to

divert some fraction of a power i.e. −10 𝑑𝐵 coupling in case of this oscillator, to the

synthesizer without interrupting much the main line power transfer.

30

Fig. 3.14 Coupled lines Directional coupler [26]

The microstrip coupler design and size depends on the choice of the substrate, height

of the substrate, dielectric permittivity, spacing between the coupled lines 𝑆, width of

the lines 𝑤 and length of the lines.

The directional coupler is linear and symmetrical in nature with the same width and

length of both the coupled lines so any port can be taken as the input port while the

port on the other side of the same arm is automatically the output. Similarly the

adjacent arm has the coupled and isolated ports. The coupled port provides the

frequency as well as a fraction of the power from the main line.

3.7 Bias Networks and Tees

There are three active semiconductor devices in the VCO’s design. These are the

VCO’s transistor, Buffer amplifier gain block and the varactor diode. All these require

a supply voltage which is fed through bias Tees.

The Bias Tee consists of a quarter wavelength transmission line which is about

7.8 𝑚𝑚 for the selected Rogers RO4003 substrate. Thus adding quarter wavelength of

line which is a short at the active device input will be open at quarter wave length

away. This is due to the fact that the quarter wavelength will move the short in is

Smith chart to open, 180 𝑜clockwise around the center of the smith chart. This

transforms the RF short circuit to RF open circuit at the other end of the quarter wave

line. The radial stub acts as a RF short and its DC open. The radial stub offers good

bandwidth compared to other stubs. Its isolates the RF from the bias tee and inducts

the DC freely.

31

3.8 Shielding

The requirements of shielding depend mainly on the use of the oscillator in a specific

application. For aerospace applications, the weight of the shield may be 10-15 % of

the total mass of the systems; a lighter shield is desired with good EMI shielding

abilities, high strength and high elasticity. In such cases metallic shields may not be

used and instead carbon composites/epoxies with some painting.

For this wave radar, the weight of the shield is not problem, as the radar is stationary

at some specific location, and the best shield may be selected which may be some

metallic shielding, like Aluminum, Copper etc. These Cu and Al have a very good

attenuation properties starting from 1 MHz and onward frequencies as in Fig. 1.1.

The metallic shielding is very efficient even in low frequency EMP. Since the shield

may be around the resonator and the oscillator circuit, so the distance is not very large

and ferrites may not be a better option than metallic shields as they are more

conductive.

32

Chapter 4 Process and Results

4.1 VCO’s Transistor Measurements

Fig. 4.1 displays the VCO’s transistor measurement test board. The transistor is

NEC’s NE685M03 and the configuration used is common base for the design of the

oscillator. The manufacturer does not provide a good model for up to 6 GHz

frequency with common base configurations, thus the measurements for the transistor

are carried out.

There is a radial stub at the base of the transistor for grounding. The measurements

are carried out through Vector Network Analyzer (VNA). The VNA is first calibrated

with Through Reflect Line (TRL) calibration method (See appendix C). The

measurement of the S parameters for the transistor with a radial stub at its base is

better characterized in this way. The transistor is supplied with a proper bias voltage.

Fig. 4.1 VCO’s transistor measurements

4.2 Attenuator Results

Fig. 4.2 shows the attenuator selected for the oscillator which is a symmetrical Pi

Network of resistors. The design is supplemented by the introduction of transmission

lines in between the resisters which are used to cancel out the reactance of the

resistors as the resisters are not perfect lumped components at very high frequencies.

33

Fig. 4.2 Schematics of the 10 dB Pi Attenuator

Fig. 4.3 S parameter simulations of the 10 dB attenuator

Fig. 4.3 shows the S parameter simulations of the 10 dB attenuator. The response is

over a frequency range of 4.8-6.8 GHz. The attenuation is with very good flatness of a

fraction of a dB over the entire frequency range. The attenuation of the attenuator i.e.

S(2,1) is 9.642 𝑑𝐵 which is close to 10 𝑑𝐵. Since the specifications of this

attenuation is very flexible, the difference of 0.4 𝑑𝐵 is not a problem at all. The S(1,2)

shows the reverse isolation of the attenuator and it is the same as S(2,1). This is due to

the fact that this design is a symmetrical Pi network.

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.64.8 6.8

-30

-20

-10

-40

0

freq, GHz

dB

(S(1

,2))

Readout

m1

dB

(S(2

,1))

dB

(S(1

,1))

Readout

m3

dB

(S(2

,2))

m1freq=dB(S(1,2))=-9.642

5.870GHz

m3freq=dB(S(1,1))=-37.311

5.870GHz

34

The reflections at the input and output of the attenuator are minimum as shown by

very low S(1,1) and S(2,2), which are −37.3 𝑑𝐵. This means that the returns loss is

very high. Again the S(1,1) and S(2,2) are both equal due to the symmetrical design of

the attenuator.

Fig. 4.4: Input and Output Impedance of the Attenuator

Fig. 4.4 shows the input and output impedance of the attenuator to be almost 50 ohms

and thus the VSWR is close to 1. This minimizes the reflections at the input and

output of the attenuator.

4.3 Buffer Amplifier

Fig. 4.5 shows the buffer amplifier schematics. The amplifier is a gain block thus it is

used directly at the output of the attenuator. The amplifier is supplied with a bias

supply of 3 𝑉 𝑎𝑛𝑑 21 𝑚𝐴. This gain block is not supplied with any input or output

matching.

freq (4.800GHz to 6.800GHz)

S(1

,1)

Readout

m2

S(2

,2)

m2freq=S(1,1)=0.014 / 21.340impedance = Z0 * (1.026 + j0.010)

5.870GHz

35

Fig. 4.5: Buffer Amplifier Schematics with 3V, 21mA bias point.

Fig. 4.6: Response of the Buffer amplifier

The Buffer amplifier response is shown in Fig. 4.6. The gain of the amplifier without

any input or output matching is about 16 dB. The most important parameter is the

reverse isolation of the amplifier S(1,2) which is −37.72 𝑑𝐵. This is the most

significant factor and very important for the oscillator along with the attenuator’s

reverse isolation. The others parameter S(2,2) is −22.14 𝑑𝐵 which is sufficient as

more than 20 𝑑𝐵 of return loss is always desirable. But the S(1,1) is just about

−5.2 𝑑𝐵 which is a bit too low.

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.84.8 7.0

-30

-20

-10

0

10

-40

20

f req, GHz

dB

(S(1

,1))

5.867G-5.271

m2

dB

(S(1

,2))

5.852G-37.72

m4

dB

(S(2

,1))

Readout

m1

dB

(S(2

,2))

5.874G-22.15

m3

nf(

2)

Readout

m7

m1freq=dB(S(2,1))=15.985

5.870GHz

m2freq=dB(S(1,1))=-5.261

5.870GHz

m3freq=dB(S(2,2))=-22.136

5.870GHz

m4freq=dB(S(1,2))=-37.721

5.870GHz

m7freq=nf(2)=1.688

5.876GHz

36

Fig. 4.7: Input and output impedance match of the buffer amplifier

The Input and output impedance match for the buffer amplifier is shown in Fig. 4.7.

The output impedance match is very good nearly 50 ohms but the input impedance

match is very poor. For the initial design, the Buffer Amplifier Gain block is used

without any input and output impedance match. This is due to the fact that the Buffer

amplifier has a very good gain of 16 dB without any matching circuit at the input or

output.

4.4 Power Supply Bias

The three active devices i.e. VCO’s transistor, varactor diode and the Buffer amplifier

is supplied with the proper bias voltage. The bias is supplied through bias tees and

Fig. 4.8 shows the schematics of bias tee. The bias tee consists of a quarter wave

transmission line which is about 7.8 mm on the Rogers 4003 substrate and a radial

stub. The layout of the bias tee is shown in Fig. 4.8.

freq (4.870GHz to 6.870GHz)

S(1

,1)

Readout

m6

S(2

,2)

Readout

m5

m6freq=S(1,1)=0.546 / -125.040impedance = Z0 * (0.365 - j0.464)

5.870GHz

m5freq=S(2,2)=0.078 / -140.330impedance = Z0 * (0.882 - j0.089)

5.870GHz

37

Fig. 4.8: Schematics of a Bias Tee

Fig. 4.9: Layout of the Bias Tee.

38

Fig. 4.10: Simulations results of the Bias Tee

The response of the bias tee is shown in Fig. 4.10. The S(2,1) is almost 0 dB which

implies that the high frequency signal is not affected by the bias Tee thus it passes

from port 1 to port 2 without any loss. The S(3,3) is also close to 0 dB which is port 3

is an RF Open and thus DC Short. Thus the RF signal will not enter the bias supply.

The value of -80 dB of the S(3,1) also confirms this. The reflections at port 1 are

minimum as S(1,1) is about -60 dB. Also at port S(1,1), the impedance is almost 50

ohms. This bias Tee is although not ideal but very much optimized and closer to ideal.

4.5 Coupler Design

The oscillator output is coupled with the synthesizer and the coupler is designed as in

Fig. 4.10. The coupler has four ports which are input, output, coupled and isolated.

The design is based on two microstrip lines coupled to each other. The isolated port is

terminated with matched impedance.

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.64.8 6.8

-0.08

-0.06

-0.04

-0.02

-0.10

0.00

freq, GHz

dB

(S(2

,1))

dB

(S(3

,3))

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.64.8 6.8

-60

-40

-80

-20

freq, GHz

dB

(S(1

,1))

dB

(S(3

,1))

Readout

m2

m2freq=dB(S(3,1))=-79.907

5.870GHzfreq (4.800GHz to 6.800GHz)

S(1

,1)

Readout

m1

S(3

,3)

S(3

,1)

m1freq=S(1,1)=0.008 / 95.719impedance = Z0 * (0.998 + j0.015)

5.780GHz

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.64.8 6.8

-100

0

100

-200

200

freq, GHz

ph

as

e(S

(3,1

))

Readout

m3

m3freq=phase(S(3,1))=-179.901

5.870GHz

39

Fig. 4.11: Schematics of 12 dB Coupler

The response of this coupler is given in Fig. 4.11. The coupled port has a coupling of

about 11.8 dB which is almost equal to 12 dB. The thru is -0.345 dB which depicts the

fact that most of the power is transmitted to the output port and only a small fraction

is sent to the coupled port. The directivity is -24.17 dB which is fairly good. The

Return loss is -29.9 dB thus there is very little reflections and the input port acts as a

matched port.

40

Fig. 4.12: Response of the 12 dB Coupler

Fig. 4.12 displays the voltage controlled coaxial resonator oscillator. The VCO’s

transistor is connected to the tuning network. The tuning network consists of the

coaxial resonator with one end shorted to ground. A varactor diode is also present in

the tuning network. The varactor and the resonator are connected through a tee and

are fed into the input of the VCO’s transistor. A 0.3 pF capacitor is also added along

the varactor diode.

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.53.5 8.0

-0.40

-0.35

-0.30

-0.25

-0.45

-0.20

freq, GHz

dB

(S(2

,1))

Readout

m1

Thru(dB)

m1freq=dB(S(2,1))=-0.345

5.870GHz

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.53.5 8.0

-13.5

-13.0

-12.5

-12.0

-11.5

-14.0

-11.0

freq, GHz

dB

(S(3

,1))

Readout

m2

Coupled Port(dB)

m2freq=dB(S(3,1))=-11.802

5.870GHz

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.53.5 8.0

-24

-23

-22

-21

-20

-25

-19

freq, GHz

dB

(S(3

,2))

Readout

m3

Directvity(dB)

m3freq=dB(S(3,2))=-24.170

5.870GHz

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.53.5 8.0

-30

-25

-20

-15

-35

-10

freq, GHz

dB

(S(1

,1))

dB

(S(2

,2))

Readout

m4

dB

(S(3

,3))

Return Loss(dB)

m4freq=dB(S(2,2))=-29.972

5.870GHz

freq (3.800GHz to 7.800GHz)

S(1

,1)

Readout

m5

m5freq=S(1,1)=0.031 / -141.241impedance = Z0 * (0.952 - j0.037)

5.870GHz

41

4.6 Voltage Controlled Oscillator (VCO) Circuit

The VCO circuit is shown in Fig. 4.13. A varactor is supplied with a variable bias

voltage which is used to tune the circuit. The VCO’s transistor is followed by an

attenuator of Pi shape. The attenuator is followed by the buffer amplifier and the

output is fed into the coupler. Fig. 4.14 displays the layout of the voltage controlled

oscillator. This layout is generated in Agilent ADS and does not include the voltage

bias circuits. This layout was imported in layout software “Mentor” and a PCB layout

was generated which contain all other components like the bias networks, connectors,

transmission lines etc.

Fig. 4.13: Schematics of the Voltage Controlled Oscillator

Fig. 4.14: Layout of the Voltage Controlled Oscillator

42

Fig. 4.15: OscTest Response of the Oscillator

These simulations are based on the OscTest component of Agilent ADS which

provides the S parameter analysis of the small signal gain (closed loop) for this

oscillator. The loop gain is represented by S(1,1) while it also measures the closed

loop phase. The oscillation is indicated by a loop gain of more than unity and the

phase at zero, while the frequency increase brings about a decrease in the phase.

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.64.8 6.8

1

2

3

4

0

5

-100

0

100

-200

200

freq, GHz

dB

(S(1

,1))

Readout

m1

phase(S

(1,1

))

Readout

m2

m1freq=dB(S(1,1))=3.716

5.570GHz

m2freq=phase(S(1,1))=-0.008

5.570GHz

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-2.0 2.0

freq (4.800GHz to 6.800GHz)

S(1

,1)

Readout

m3

m3freq=S(1,1)=1.534 / -0.008

5.570GHz

43

The Agilent ADS simulations of the VCO are given in Fig. 4.15. The oscillator has

S(1,1) greater than unity at the 5.57 GHz while the phase at this frequency is almost

zero. Thus this is the oscillation frequency with a varactor bias voltage of 4 volts.

The Table 4.1 displays the results of simulations of the VCO. The varactor diode bias

voltage is selected from 4-18 volts with increments of 2 volts, which is the standard

operating voltage for Microsemi MPV2100 varactor diodes. The oscillation frequency

starts at 5.57 GHz at 4 volts of varactor voltage and reaches 5.636 GHz at a voltage of

18 volts. This gives a total tuning voltage of 80 volts.

Serial Number Varactor bias voltage

(volts)

Oscillation frequency

(GHz)

1 0 5.538

2 4 5.557

3 6 5.582

4 8 5.587

5 10 5.601

6 12 5.610

7 14 5.619

8 16 5.628

9 18 5.636

Table 4.1: Oscillation Frequency of VCO as a function of varactor bias voltage

44

4.7 Fabrications and Measurements

Fig. 4.16: PCB of the VCO

Fig. 4.16 shows the fabricated coaxial resonator oscillator. The results show that the

oscillator oscillates at 5.54 GHz in the absence of the 0.3 pF capacitor and the

varactor diode. This is almost very close to the designed frequency of oscillation. The

output power is 3.83 dBm measured though a spectrum Analyzer as shown in Fig.

4.17. It’s a bit lower than the expected 7 dBm for the specifications.

When the 0.3 pF capacitor is added with the resonator, the frequency of oscillation of

the VCO drops to 5.45 GHz while the output power is 4 dBm. Finally the varactor

diode is soldered and the results are obtained as in the Table 4.2.

45

Fig. 4.17: VCO measurements through Spectrum Analyzer

Serial Number Varactor bias

voltage

(volts)

Oscillation

frequency

(GHz)

Output Power

(dBm)

1 0 5.230 4

2 4 5.270 4

3 6 5.290 3.83

4 8 5.300 3.83

5 10 5.314 3.83

6 12 5.324 3.67

7 14 5.333 3.83

8 16 5.340 3.83

9 18 5.345 3.50

Table 4.2: Results of the VCO for the Varactor tuning

Table 4.2 show that the VCO has almost constant power of around 4 dBm. The tuning

range is 75 MHz which is good enough for the design.

46

𝑇𝑒𝑚𝑝 = 0𝑜𝐶 𝑇𝑒𝑚𝑝 = 20𝑜𝐶 𝑇𝑒𝑚𝑝 = 40𝑜 𝑇𝑒𝑚𝑝 = 60𝑜

S

No

.

𝑉𝑣𝑎𝑟

(𝑣𝑜𝑙𝑡𝑠)

𝑓𝑜

(𝐺𝐻𝑧)

𝑃𝑂𝑈𝑇

(𝑑𝐵𝑚)

𝑓𝑜

(𝐺𝐻𝑧)

𝑃𝑂𝑈𝑇

(𝑑𝐵𝑚)

𝑓𝑜

(𝐺𝐻𝑧)

𝑃𝑂𝑈𝑇

(𝑑𝐵𝑚)

𝑓𝑜

(𝐺𝐻𝑧)

𝑃𝑂𝑈𝑇

(𝑑𝐵𝑚)

1 4 5.285 4.17 5.279 3.67 5.271 3.67 5.254 3.13

2 6 5.300 4.33 5.292 3.67 5.283 3.67 5.274 3.33

3 8 5.313 4.17 5.305 3.83 5.295 4.00 5.284 3.13

4 10 5.327 4.33 5.317 4.17 5.305 3.5 5.293 3.13

5 12 5.337 4.17 5.328 4.17 5.314 3.67 5.305 3.5

6 14 5.346 4.00 5.337 4.17 5.325 3.84 5.312 3.5

7 16 5.354 3.53 5.345 4.00 5.334 3.83 5.319 3.5

8 18 5.357 4.00 5.347 3.83 5.337 3.83 5.340 3.67

Table 4.3 Results of the VCO over a Temperature Range

where

𝑓𝑜 = 𝑂𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛 𝐹𝑟𝑒𝑞𝑢𝑒𝑐𝑛𝑦 𝑜𝑓 𝑡𝑕𝑒 𝑉𝐶𝑂 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑖𝑛 𝐺𝐻𝑧

𝑉𝑣𝑎𝑟 = 𝐵𝑖𝑎𝑠 𝑣𝑜𝑙𝑎𝑡𝑔𝑒 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑡𝑜 𝑡𝑕𝑒 𝑣𝑎𝑟𝑎𝑐𝑡𝑜𝑟 𝑑𝑖𝑜𝑑𝑒 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑖𝑛 𝑣𝑜𝑙𝑡𝑠

𝑃𝑂𝑈𝑇 = 𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑡𝑕𝑒 𝑉𝐶𝑂 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑖𝑛 𝑑𝐵𝑚

Table 4.3 displays the temperature performance of the oscillator. The

temperature is selected from 0𝑜 to 60𝑜 which induces a shift of the frequency

about 30 MHz.

Phase Noise Measurements

The phase noise of this oscillator is −88 𝑑𝐵𝑚/𝐻𝑧 𝑎𝑡 50 𝑘𝐻𝑧 offset from

4 𝑑𝐵𝑚 carrier or −92 𝑑𝐵𝑐/𝐻𝑧. At 100 kHz offset the phase noise is

−94 𝑑𝐵𝑚/𝐻𝑧 ( −98 𝑑𝐵𝑐/𝐻𝑧).

47

Load Pull Measurements

Figure 4.1 shows the Load Pull measurement setup, with the DUT attached to

the cable having 1.5 dB loss, and a 3 dB attenuator. The attenuator is

connected to -10 dB approximately. The coupled port is connected to the

Spectrum Analyzer while the thru port is connected to the Line Stretcher

which is open circuit at other end.

Fig. 4.18: Load Pull measurements

The measurement shows that with a return loss of the setup equal to almost 12

dB, and with a change of phase from 0− 180𝑜 , a 1MHz of frequency pulling

is calculated.

The results were a bit different from the expected simulations. The biggest

cause was that the resonator layout was incorrectly perceived, and it pulled the

frequency about 300 MHz down from its target of 5.87 MHz. This was due to

incorrect layout realization due to which the exact frequency of 6.2 GHz was

not achieved. This calls for a need to make test circuits for the resonator and

the test it using one port VNA measurements. Thus the S Parameters obtained

this way can be used in the simulations.

48

Chapter 5 Discussions & Conclusions

Table 4.1 shows simulations of the varactor diode tuning and the resulting

frequency response in GHz. The varactor diode has an operating voltage range

from 4 to 18 volts. This will give a tuning range of

𝑇𝑢𝑛𝑖𝑛𝑔 𝑅𝑎𝑛𝑔𝑒 = 5.557 𝐺𝐻𝑧 − 5.636 𝐺𝐻𝑧 = 79 𝑀𝐻𝑧

The printed board measurements through a spectrum Analyzer showed the

tuning range as

𝑇𝑢𝑛𝑖𝑛𝑔 𝑅𝑎𝑛𝑔𝑒 = 5.270 𝐺𝐻𝑧 − 5.345 𝐺𝐻𝑧 = 75 𝑀𝐻𝑧

This shows a very good result of the tuning range as the 75-80 MHz tuning is

sufficient for the products at the company.

The capacitor in series with the varactor diode has a value of 0.3 pF in the VCO

design. This value is varied and some new results have been obtained as given in

Table 5.1. If this capacitor is not included, the OscTest S(1,1) phase is at zero but the

S(1,1) is not at maximum. In some cases the tuning range is very low if this capacitor

is not added. Thus the capacitor is added to the design. The value of the capacitor is

varied and results obtained in Table 5.1. These results show that the increase in the

capacitance increases the tuning range.

S. No Capacitor

(pF)

Frequency

(at 4 volts)

Frequency

(at 18 volts)

Tuning

frequency

range

1 0.1 5.765 5.775 10 MHz

2 0.2 5.664 5.694 30 MHz

3 0.3 5.574 5.634 60 MHz

4 0.4 5.493 5.574 81 MHz

5 0.5 5.433 5.544 111 MHz

Table 5.1 Tuning range results with varying capacitor values

49

There is another problem with this capacitor, as its value is too low i.e. 0.3 pF. The

high tolerance of this capacitor will increase the uncertainty. The parasitic reactance

could also be appreciable due to the manufacturing, soldering and mounting of the

components. Simulations have shown that increasing this capacitor value can increase

the tuning range but then a very high value capacitor value in the tuning network will

shift the oscillation frequency down which is not desirable. Thus a trade off was made

and a capacitor value was suggested and used.

The design of oscillator gave a low output power of around 3.5-4 dBm which is lower

than the expectations of the 7 dBm. In the previous design, no matching network was

used for the buffer amplifier although its input had a very bad match. Thus the input

of the buffer amplifier has to be matched with a matching network, to achieve a

higher gain.

Fig. 5.1 shows that the input is matched and the gain of the amplifier is 17.5 dB which

is 1.5 dB higher. Also the Smith chart shows the input and output match to be around

50 ohms.

Fig. 5.1 Schematics for Matching Network of the Buffer Amplifier

50

Fig. 5.2 Results of the Matching Network of Buffer Amplifier

There is an uncertainty with the resonator modeling and characterization as well. The

resonator data was taken from the manufacturer datasheets and a parallel RLC model

was created as shown in Fig. 3.7 and 3.8. The model showed perfect match with the

manufacturer data sheet values.

The manufacturer provided the resonator’s recommended pad for mounting on the

PCB as seen in Fig. 5.3. One end is shorted and the other end is connected to the

varactor tuning network through a Tee that leads into the transistor.

Fig. 5.3 Recommended pad for the Resonator

5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.84.8 7.0

-40

-30

-20

-10

0

10

-50

20

f req, GHz

dB

(S(1

,1))

Readout

m2

dB

(S(1

,2))

Readout

m4

dB

(S(2

,1))

Readout

m1

dB

(S(2

,2))

Readout

m3

m2freq=dB(S(1,1))=-30.917

5.870GHz

m4freq=dB(S(1,2))=-36.203

5.870GHz

m1freq=dB(S(2,1))=17.503

5.870GHz

m3freq=dB(S(2,2))=-19.050

5.870GHz

f req (4.870GHz to 6.870GHz)

S(1

,1)

Readout

m6

S(2

,2)

Readout

m5

m6freq=S(1,1)=0.028 / 146.630impedance = Z0 * (0.953 + j0.030)

5.870GHz

m5freq=S(2,2)=0.112 / -104.515impedance = Z0 * (0.924 - j0.202)

5.870GHz

51

Simulating again the model as in Fig. 3.9 and 3.10 shows that the addition of the pads

pulled the resonator frequency down to 5.137 GHz, which is about 1 GHz less than

the resonator original frequency.

Another approach to characterize the resonator network is to take one port

measurements of the resonator and then use these measurements in the simulations.

S parameters were extracted and simulated as in Fig. 5.4 and 5.5. This showed that the

resonance frequency at 6.63 GHz. This method characterizes the resonator along with

the pads.

Fig. 5.4 Resonator with Pads, One Port Test circuit

Fig. 5.5 One Port Measurements of the Resonator

5.0 5.5 6.0 6.5 7.0 7.54.5 8.0

-5

-4

-3

-2

-1

0

-6

1

freq, GHz

dB

(S(1

,1))

6.630G-5.204

m1

m1freq=dB(S(1,1))=-5.204

6.630GHz

52

The manufacturer provided 10 samples and they were about at maximum 30 MHz

offset from the resonator’s 6.2 GHz frequency. So this tolerance has to be taken into

consideration as well.

The attenuator design was according to specifications. The input and output match

were almost 50 ohms thus the VSWR is close to 1. The output of the attenuator is fed

to the input of buffer amplifier, thus the matching is preserved and the buffer

amplifier provides very good gain and high reverse isolation. The flatness is just a

fraction of a dB for a 2 GHz frequency range which is perfect.

The comparative study of this oscillator design with the state of the art studies is

described. Comparing with [1], where a state of the art phase locked DRO/CRO is

presented, with a phase noise 𝑜𝑓 − 120 𝑑𝐵𝑐/𝐻𝑧 𝑎𝑡 100 𝐾𝐻𝑧 offset from carrier.

The phase noise of our oscillator at 100 KHz offset is 94 𝑑𝐵𝑚/𝐻𝑧 (−98 𝑑𝐵𝑐/

𝐻𝑧 𝑎𝑠 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑝𝑜𝑤𝑒𝑟 𝑖𝑠 4 𝑑𝐵𝑚). There is a difference of 22 dB and this may be

due to several facts. One of the reasons is that it is only the VCO design, and it’s not

phase locked CRO. The 2nd

reason is that the resonator layout pad was not designed as

recommended by the manufacturer and this pulled the frequency down. The bias Tees,

attenuator, and all other circuits were optimized for the 5.87 GHz, which may have

contributed to this phase noise. Thus approximating, this VCO will provide almost the

same response of the phase noise as in [1], when the resonator layout pads is correctly

designed and measured to provide the 6.2 𝐺𝐻𝑧 as specified by the manufacturer.

In [9], where the range of a varactor diode is increased by more than 10 times, by the

introduction of the negative capacitance connected to the varactor. The negative

capacitance is created by two common source transistors, loaded with inductors. The

table 5.1 describes the tuning characteristics of the varactor in the presence of a small

capacitor connected to the varactor. The increase in the capacitance increases the

tuning range by 10 times by increasing the value of this capacitance.

In [11], the frequency stability is 130 ppm without any temperature compensation

from −50𝑜𝐶 𝑡𝑜 +50𝑜 𝐶. The variation in output power at −50𝑜𝐶 is

+35 𝑑𝐵𝑚 (3.2 𝑊) and at +50𝑜 𝐶 was 33 𝑑𝐵𝑚 (2 𝑊) which shows the temperature

stability of the DROs. Comparing, the Table 1.3, shows that from 0− 60𝑜 𝐶 , the

change in output power is about 0.5-1 dBm, which is relatively stable with the change

of temperature.

53

In [12], a very linear MIC bipolar VCO with 100 MHz FM rate s described with

frequency pulling is ± 1 𝑀𝐻𝑧 into a 2:1 mismatched load. The total load isolation

achieved is more than 45 dB. The FET amplifier provides 35 dB of isolation while 12

dB of isolation is provided by a thin film pi attenuator. Comparatively, this oscillator

achieves almost the same results with a total isolation of about 47 dB, and a 1 MHz

frequency pull due to load and with 10 𝑑𝐵 coupler and a variation of 0− 180𝑜 phase

change.

In [15], he experimental results predicts that the residual phase noise of the HBT

based oscillators is a function of the bias dependant LF noise up conversion factor of

the device. This concludes that for a low phase noise, the two important decisions are

device selection and matching network design. Since the resonator layout was

mistakenly incorrect, and shifted the frequency of the resonator to about 350 MHz,

the Bias Tees and other circuits designed for the original frequency or 5.87 MHz,

were not matched, thus it is may have contributed to the phase noise also.

54

Chapter 6 Future Work

The Agilent ADS simulations, as seen in Fig. 4.15 show that the oscillator is

oscillating at 5.57 GHz of frequency. This is the 1st test board where there were some

uncertainties. Thus the next version of this oscillator will be designed to oscillate at

5.87 GHz as the product specifications. This would mean that the uncertainty of the

resonator layout will be removed by careful design and testing.

The capacitor in series with the varactor diode should have an optimized value that

could give us a very good tuning frequency range. The uncertainties regarding the low

value of the capacitance, component tolerances and manufacturing parasitic

reactances are to be removed. This can be done by a design which uses a capacitor

with 0.5-1 pF capacitor. This increase in bandwidth could also make it useful for other

frequencies within the band.

The next version of the oscillator will have the Phase Locked Loops (PLL) by the

introduction of the synthesizer and microcontroller. The size of the microstrip lines

will be reduced by some adjustments to the resonator network. This could improve the

power out of the VCO transistor.

At last, the simple bias will be replaced by a bias which produces minimum spurious

and phase noise. This can improve the phase noise performance of the oscillator. This

can be realized by having very high capacitance, de-coupling capacitors in the supply

to filter out the noise.

55

References

[1] B. Hitch and T. Holden, “Phase Locked DRO/CRO for Space use”, IEEE

International Frequency Control Symposium, pp. 1015-1023. May 1997.

[2] U. L. Rohde and A. K. Poddar, “Novel Multi-Coupled Line Resonators Replace

Traditional Ceramic Resonators in Oscillators/VCOs”, IEEE International

Frequency Control Symposium and Exposition, pp. 432-442, June 2006.

[3] X. Wang and H.Wang, “The Innovative Research of Integrating Electromagnetic

Shield into Three- Dimensional Circuit”, in Seventh International Conference on

Electronic Packaging Technology, pp. 1-7, Aug. 2006.

[4] S. Miyake, Y. Umezu, Y. Sagawa, T. Morita, and R. Yoshino, “Investigation

related to Construction Method and Performance of an Electromagnetic

Shielded Enclosure”, IEEE International Symposium on Electromagnetic

Compatibility, pp. 120-125, Aug. 1991.

[5] J. R. Gajer, “Intercalated Graphite Fiber Composites as EMI Shields in

Aerospace Structures” IEEE Transactions on Electromagnetic Compatibility,

vol 34, no. 3, part 1, pp. 351-356, Aug. 1992.

[6] S. R. Ramasamy and Devender, “A Review of EMI Shielding and Suppression

Materials” In the Proceedings of the International Conference on

electromagnetic Interference and Compatibility, pp. 459-466, Dec. 2007.

[7] C. A. Grimes and D. M. Grimes, “A Brief Discussion of EMI Shielding

Materials”, IEEE Aerospace Applications Conference, Dig. , pp. 217-226,

1993.

[8] F. Lawrence, Babcock, “Shielding Circuits from EMP” IEEE Transactions on

Electromagnetic Compatibility, vol. 9, no. 2, pp. 45-48, Sept. 1967.

[9] S. Koley, B. Delacressonniere, J.-L. Gautier, “Using a Negative capacitance to

increase the tuning range of the varactor diode in MMIC Technology”, IEEE

Transactions on Microwave Theory and Techniques, vol. 49, no. 12, Dec. 2001.

[10] P. Stockwell, D. Green, C. McNeilage and J. H. Searls, “A Low Phase Noise

1.3 GHz Dielectric Resonator Oscillator”, IEEE International Frequency

Control Symposium and Exposition, pp. 882-885, June 2006.

[11] M. Mizan, D. Sturzebecher, T. Higgins and A. Paolella, “An X- Band, High

Power Dielectric Resonator Oscillator for Future Military Systems”, IEEE

Transactions on Ferroelectrics and Frequency Control, vol. 40, no. 5, pp.

483-487, Sept. 993.

56

[12] R. G. Winch and J. L. Matson, “Very Linear X-Band MIC Bipolar VCO with

100 MHz Rate”, MTT-S International Microwave Symposium, Dig. vol. 80,

pp. 499-500, May 1980.

[13] R. Spence, “A Transistor Oscillator Frequency Stability Study”, IRE

Transactions on Circuit Theory, vol. 9, no. 2, pp. 110-115, June 1962.

[14] J. J. Ebers and S. L. Miller, “Design of Alloyed Junction Germanium

Transistors for High-Speed Switching”, Bell Sys. Tech. J., vol. 34 761-781,

July 1955.

[15] X. Zhang and A. S Daryoush, “Bias Dependant Noise UP-Conversion Factor in

HBT Oscillator”, IEEE Microwave and Guided Wave Letters, vol. 4, no. 12,

pp. 423-425, Dec. 1994.

[16] D. Usanov, A. Skripal, A. Abramov and V. Pozdnyakov, “ Semiconductor

Microwave Oscillators Controlled by the Bias Point Voltage”, pp. 13-17,

Sept. 2004.

[17] RFIC Theory Tutorials, August 2008, www.rfic.co.uk

[18] U. L. Rhode, A. K. Poddar and G. Bock, “The Design of Modern Microwave

Oscillators for Wireless Applications”, John Wiley & Sons,Inc. New Jersey,

2005.

[19] J. Tang and D. Kasperkovitz, “High Frequency Oscillator Design for Integrated

Transceivers”, Kluwer Academic Publishers, New York.

[20] Agilent Technologies, “Attenuator Overview”, April 2008.

[21] H. Kinley, “Demystifying RF Attenuators” Urgent Communications, Nov 1,

2004.

[22] High Frequency Electronics, “Basic Data on High Q Ceramic Coaxial

Resonators” Summit Technical Media, LLC, November 2002.

[23] Skyworks, Appli. Note No 1008, “Coaxial Resonator for VCO Applications”.

[24] Skyworks, Appli. Note No 1010, “Frequency Tuning of Coaxial Resonators”.

March 9, 2007.

[25] MicroMetrics, Appl. Note, “Tuning Varactors” May 2008.

http://www.micrometrics.com/pdfs/TV_AppNotes.pdf

[26] Directional Coupler, July 2008,

www.ee.bilkent.edu.tr/~microwave/programs/magnetic/dcoupler/theory.htm

57

Appendix A

IMC Resonators

The resonators selected for the oscillator are coaxial resonators from Integrated

Microwaves Corporation (IMC). The selected resonator for the design is about 4

𝑚𝑚2 in size. Fig. below shows the resonator dimensions where the inner diameter is

1.14 mm. The length of the resonator is 4.27 mm.

Fig. 4.16 Dimensions of the IMC resonator 4 𝒎𝒎𝟐 coaxial resonators.

The software provided by IMC simulates the 4 𝑚𝑚2 quarter wave shorted resonators.

The impedance response vs. frequency is given as in Fig. 4.17. The impedance is

highest at the 6.2 GHz.

Fig. 4.17 Impedance vs. frequency response of the coaxial resonator

The phase response is given in Fig. 4.18.

58

Fig. 4.18 Phase response of the IMC resonators

The tolerance of the resonator is± 1 %. The 10 sample resonators acquired from the

IMC were having about ± 0.5− 0.7 % of tolerance which is inside the manufacturer

specifications. The resonator selected was a without the tab. Further the resonators are

ceramic in nature.

The following characteristics are for the resonator, supplied by manufacturer.

𝐷𝑖𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 휀 = 8

𝑄𝑢𝑎𝑙𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 = 𝑄 = 720

𝑍𝑜 = 28.03 Ω

𝑅 = 25696.01 Ω

𝐿 = 0.9161 𝑛𝐻

𝐶 = 0.7193 𝑝𝐹

59

Appendix B

Recommended Layout for Resonator

These Figures show the recommended pads layout for the dielectric coaxial resonator

supplied by IMC.

60

Appendix C

TRL Calibrations

These Figures describe the Through Reflect Line test circuits that were used to

calibrate the VNA.

Through

Reflect

Line