CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

Negative Resistance Oscillator Design at 16 GHz

A Graduate Project Submitted in the Partial fulfilment of the Requirements

For the degree of Master of Science in Electrical Engineering

By,

Ashwini Anil Latne

May 2017

The Graduate Project of Ashwini Anil Latne is approved:

______

Prof. Benjamin F. Mallard Date

______

Dr. John Valdovinos Date

______

Dr. Matthew M. Radmanesh, chair Date

California State University, Northridge

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Acknowledgement

It gives great pleasure to acknowledge the sense of gratitude to all those who helped me in making “Negative resistance oscillator design” project a success. It has been immense pleasure to work under supervision of Prof. Matthew Radmanesh to complete this project. I am deeply obliged to Prof. Matthew Radmanesh for his invaluable guidance, encouragement and support that I received throughout my project.

I would like to thank Prof. Matthew Radmanesh for being my graduate advisor and helping me in completing my graduate project. His courses like Active Microwave Circuit Design and Advanced Microwave Circuit Design has helped me to understand many concepts of design which were useful for my project. The basic concepts of design from his book named “RF and Microwave Design Essentials” helped me in completing my project.

I want to thank my committee members Prof. Benjamin Mallard and Dr. John Valdovinos for their advice and valuable time.

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Table of Contents

Signature page ii

Acknowledgement iii

List of the Figures vi

List of Tables vii

Abstract viii

Chapter 1: Introduction 1

1.1: Design Specifications 1

1.2: Organization of report 2

Chapter 2: Oscillator Design Theory 3

5

2.3: Negative Resistance Oscillator Design Theory 7

2.4: DC Biasing of NPN Transistor 10

Chapter 3: Negative Resistance Oscillator Design 13

13

3.2: Oscillation Conditions 15

3.3: Stability Check 17

3.4: Output Stability Circle 18

21

3.6: Design of Negative Resistance Oscillator 22

3.7: Generator Tuning Network Design 24

3.8: Terminating Tuning Network Design 26

3.9: Microstrip Line Design 29

Chapter 4: AWR Microwave Office 35

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Chapter 5: Summary 36

5.1: Conclusion 36

References 38

Appendix A: Circuit design using lumped elements 39

Appendix B: CD ROM calculations 44

Appendix C: MATLAB program for oscillator design 48

Appendix D: MATLAB program for microstrip line design 50

Appendix E: Roger’s corporation RO3035 52

Appendix F: Datasheet of NE661M04 Transistor 54

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List of Figures

Figure 1.1: Block diagram of Negative Resistance Oscillator 1

Figure 2.1: Two-port oscillator block diagram 3

Figure 2.2: NPN Transistor 5

Figure 2.3: Voltage and current in negative resistance device 7

7

Figure 2.5: Circuit diagram of DC biasing of BJT 10

Figure 3.1: Negative resistance oscillator circuit 14

Figure 3.2: Two-port oscillator design conditions 16

Figure 3.3: Plot of stability circle on smith chart 20

Figure 3.4: Generator tuning network design on smith chart 24

Figure 3.5: Terminating tuning network design on smith chart 26

Figure 3.6: Circuit diagram 28

29

Figure 3.8: Electric and magnetic field lines 29

Figure 3.9: Layout of the circuit 34

Figure 4.1: Circuit layout 35

Figure 4.2: |S21| graph 35

Figure A1: Generator tuning network (lumped elements) 40

Figure A2: Terminating tuning network (lumped elements) 42

Figure A3: Circuit layout (lumped elements) 43

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Table 3.5.1: Selection of the ΓT 21

Table 3.6.1: Value of Zin 22

Table 3.9.1: Microstrip line results 33

Table 5.1: Summary of results 37

vii

Abstract

NEGATIVE RESISTANCE OSCILLATOR DESIGN AT 16 GHz

By,

Ashwini Anil Latne

Master of Science in Electrical Engineering

This project explores the design process of Negative Resistance Oscillator operating at 16GHz which has many microwave applications. An NE661M04 BJT is selected to achieve requirements of the transistor used for negative resistance oscillator design. The transistor satisfies the oscillation conditions. Then the output stability circle is plotted using S-Parameters from the datasheet of transistor. Using an output stability circle, the generating tuning network and matching tuning network is plotted on the smith chart. The value of negative resistance is then determined from the smith chart. The calculations for the design process are also calculated theoretically. Smith chart values and theoretical values are verified using MATLAB software.

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Chapter 1: Introduction

An oscillator is an important part of any microwave communication system, since it can convert DC power to microwave power. An oscillator is designed to convert a DC signal to RF signal, thus it forms an important device of the microwave system. To design one port negative resistance oscillator, a two-terminal device is used. Oscillators are mainly used in microwave applications like satellite receivers, radar speed gun, radar transmitters and microwave ovens. Oscillators can also be used in circuits of feedback oscillators along with two port devices like transistor and tubes. Oscillators are also used in electronic devices like TV, radio, cell phone, modems and computers.

Figure 1: Block diagram of Negative Resistance Oscillator

1.1 Design specifications:

Transistor:

Operating frequency: 16 GHz.

Output power: <5dBm

1

1.2 Organization of Report:

Chapter 1: Introduction

Chapter 2: Oscillator design theory

Chapter 3: Negative Resistance Oscillator Design

Chapter 4: Simulation Results

Chapter 5: Conclusion

2

Chapter 2: Oscillator Design Theory

2.1 Review of Literature

RF and microwave oscillators has many applications in wireless communications, remote sensing systems and radar, since it provides high signal sources to convert frequency and carrier signal generation. At high frequencies, using diodes and transistors with cavity can produce fundamental frequency oscillations up to 100GHz. Using transistors in the oscillators is more compatible than diode, since it is easy to integrate transistors with amplifiers and mixers in the circuits. Transistors allow more control on frequency oscillation, output noise and temperature stability. They are also useful to frequency tuning, phase and injection locking.

An RF/microwave oscillator is a non-linear circuit that converts DC power to microwave power. In this project, a three-terminal device is used which provides two-port oscillators and is operated in an unstable region.

Figure 2.1: Two-port oscillator block diagram

3

The design steps for oscillator are like that of the microwave amplifier. The main difference between the two is that design of the amplifier requires microwave signal as an input, but oscillator design does not require any input. To design oscillator, first we select the transistor, whose S-parameters satisfies the condition for oscillation. Since power is generated in an oscillator, the reflections are greater than unity. Thus, we require compressed smith chart for the oscillator design process. Then, the generator tuning network and terminating tuning network are designed using smith chart.

The generator tuning network in design gives the oscillation frequency, whereas the terminating network gives the proper loading function. Since, it is a non-linear device, the complete analysis of oscillator operation is complicated. The circuit is built using distributed elements for high frequency. The hand calculations result and smith chart values are verified on MATLAB.

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2.2 Transistor selection

A transistor, in general, is a nonlinear three terminal devices in which the flow of current between terminals is controlled by the third terminal. It is used mainly in amplifiers, oscillators, switches and detectors. There are two classes of transistors,

In this project, we have used BJT NE661M04. It is an NPN silicon high frequency transistor.

Figure 2.2: NPN Transistor

Bipolar Junction Transistors consist of three layers of semiconductors and two junctions. The semiconductor layers can be of N-type or P-type. Thus, BJT can be NPN or PNP. The three terminals of the transistor are called emitter, base and collector and two junctions are called emitter base junction (EBJ), and the collector base junction (CBJ). To use the transistor, we must do DC biasing of the transistor. That is, we must find DC bias values of the transistor. Based on the biasing conditions on each of the two junctions there can be four modes of operation of the transistor. It can be a forward biased or reverse biased.

NEC’s NE 661M04 are fabricated on wafer using NEC’s UHS0 25 GHz fT wafer process. Thus, NE661M04 provides better low voltage and low current performance. NEC’s today is used in many wireless applications. An NE661M04 is a preferred choice for design of LNA and Oscillator and has many requirements in mobile communications.

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The transistor is selected such a that its S-parameters should satisfy the oscillation conditions. There are three conditions required to be satisfied at “steady state” for an oscillation to occur. The conditions are,

Condition 1: It should be an unstable device.

K<1.

Condition 2: Oscillating input port.

ΓinΓg=1.

Condition 3: Oscillating output port.

ΓoutΓt=1.

Where, condition 1 indicates that the negative resistance device itself is in the oscillation mode.

Since, these conditions are satisfied, NE661M04 transistor is used in the design process.

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2.3 Negative Resistance Oscillator Design Theory

To design a Negative Resistance Oscillator, we need to understand negative resistance device. The concept of the negative resistance device is directly related to the concept of the power generation which is important for oscillator to work.

In negative resistance, the voltage and current are 180 degrees out of phase. Thus, an increase in voltage in negative resistance device leads to decrease in current and product of voltage and current becomes negative. This corresponds to the concept of power generation.

Figure 2.3: Voltage and current in the negative resistance device

Negative resistance oscillator design uses transistor that can operate in an unstable region.

Figure 2.4: A Negative resistance oscillator block diagram

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Here,

[S] = S- parameters of transistor

In the two-port oscillator, the mostly consists of load and that with the transistor provides the necessary negative resistance to the circuit. Whereas, the Generator tuning network determines the oscillation frequency using a resonator or impedance matched circuit.

For the two-port device to oscillate, it should satisfy the following conditions,

Condition 1: Unstable transistor device

K < 1

Where,

Condition 2: Oscillating generator input port

Condition 3: Oscillating terminating output port

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Condition 2 and condition 3 are dependent on each other. Condition 2 is satisfied only if condition 3 is satisfied. Also, the below conditions are verified.

|훤푇| and |훤푔| < 1

The conditions obtained from the above for two-port devices should also satisfy the oscillation conditions.

Thus,

(푍푔 + 푍푖푛) < 0 (steady state)

(푅푔 + 푅푖푛) < 0 (steady state) and (푋푔 + 푋푖푛) = 0

Therefore, while designing oscillator the generator tuning resistance should be choosing such rd that the value is 1/3 of the input port resistance (|푅푖푛|/3). Then the phase components should be

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2.4 DC biasing of the NPN transistor

DC biasing plays an important role in the proper functioning of the circuit. DC biasing is defined as setting DC voltages at each of the two junctions (EBJ or CBJ) such that the transistor will perform unstably in the intended mode. By setting the desired values for each of the two- transistor junction, voltages can be translated equivalently into terminal current values such as emitter and collector currents which can be then used to specify the DC bias values of the transistor. These currents in conjunction along with the DC bias voltage values of junctions satisfy the desired specifications of a transistor.

In DC biasing, we determine the transistor’s operating currents and voltages which are,퐼퐵푄,

퐼퐶푄, 퐼퐸푄, 푉퐶퐸푄, and 푉퐶퐵푄 by knowing the value of β.

Figure 2.5: Circuit diagram of DC biasing of BJT

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DC biasing of BJT

β = 70 (from datasheet)

ICQ = 5mA

VCEQ = 2v

VCC = 6v

ICQ = α IEQ

Where,

β α = 1+β

= 0.986

Thus,

5mA = 0.986 IEQ

IEQ = 5.07mA

I I = CQ BQ β

5mA = 70

= 0.071mA

As a rule of thumb, VB is selected to be one-third of the power supply voltage,

VB = 6/3 = 2v

Assuming R1 = 4kΩ, we obtain R2 as follows,

R1 = 4kΩ

VB = Vcc × R2/ (R1+ R2)

2 = 6 × R2/ (4 +R2 )

R2 = 2kΩ

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VE = VB – 0.7 = 1.3v

RE = VE/IEQ

RE = 0.26kΩ

VCC = RCICQ + VCEQ + REIEQ

RC = (6-2-1.3)/5.07mA

RC = 0.53kΩ

Verification: In order to use voltage division rule we require I1 >> IB

I1 = VCC/6k = 1mA >> IB = 0.071mA

Therefore, we are justified in using voltage division rule.

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Chapter 3: Negative Resistance Oscillator Design

3.1: Design Procedure for Oscillator

To design an oscillator, we have used two-port negative oscillator design technique. In this technique, S-parameters are used to characterize the transistor. In this design, the transistor is treated as a negative resistance device and then the oscillator can be designed.

First, we select the transistor that is potentially unstable at the desired frequency of the oscillation. Further, the transistor is terminated using an appropriate load value in the unstable region, such that it gives largest possible negative resistance at the input of the transistor. Finally, the generator tuning network is selected such that it satisfies the oscillation start-up condition.

Based on the above discussion, the design steps for oscillator are as follows:

1. Select a transistor that is potentially unstable at the desired frequency of oscillation. 2. Select a proper transistor circuit configuration,

a. For Bipolar Junction Transistors: common base or common emitter. b. For Field Effect Transistor: common gate or common source.

3. Plot the output stability circle in the ΓT- plane, using the smith chart. 4. Select a proper value for ΓT in the unstable region to produce a negative resistance at the input of the transistor (should be large).

|Γin| > 1 => Zin < 0

5. Choose appropriate value of generator tuning network impedance (Zg), such that:

6. To satisfy the oscillation condition, a typical value of Rg is chosen such that,

Rg = |Rin|/3, Rin < 0

7. The reactive part of Zg is selected to resonant the circuit:

13

Xg = - Xin

8. The generator and terminating matching networks are designed using distributed elements technique.

Figure 3.1: Negative resistance oscillator circuit

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3.2: Oscillation Conditions

Two-port negative resistance oscillators

There are three main conditions that needs to be satisfied in “steady state” for oscillations to occur.

a. Condition 1: Unstable device

K < 1

b. Condition 2: Oscillating input port

ΓinΓg = 1

c. Condition 3: Oscillating output port

ΓoutΓT = 1

Where “K”, “Δ”, Γin, Γout is given by,

Condition 1 indicates that negative resistance device itself is in oscillation mode.

Condition 2 and condition 3 are dependent on each other. That is, condition 2 is satisfied only if condition 3 is satisfied. This dependency indicates that if one port is oscillating then the other port also oscillates.

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Since, the generator-tuning and load-matching network are passive, we have,

|Γg| < 1

|ΓT| < 1

Thus, to satisfy condition 2 and condition 3, we need to have,

|Γin| > 1

|Γout| > 1

Hence, these conditions confirm condition 1 (which is required for device to be in unstable state) and this indicates an oscillator design. This shows the use of compressed smith chart.

Figure 3.2: Two-port oscillator design conditions

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3.3 Stability check

The S-parameters of the transistor (from datasheet) at16 GHz are,

S11 = 0.732 ˪ -64.5°

S21 = 0.963 ˪ -176.4°

S12 = 0.221 ˪ -91.0°

S22 = 0.488 ˪ 106.8°

To check stability conditions, we calculate the determinants of s-matrix ‘Δ’ and stability factor ‘K’ as follows,

Where,

Δ = (0.732 ˪ -64.5°) × ( 0.488 ˪ 106.8°)- (0.221 ˪ -91.0°) × (0.963 ˪ -176.4°)

= 0.275 ˪ 5.73°

|Δ| = 0.275

Thus, |Δ| < 1

1−(0.732)2−(0.488)2+(0.275)2 K = 2∗(0.21)

K = 0.71

Thus, K < 1

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3.4 Output Stability Circle

The output stability circles indicate the boundaries between “stable” and “unstable” regions for the different values of ΓL and ΓT. When there are passive matching networks, these values

.

Here, the output stability circles are plotted in the 훤퐿-plane. If we set 훤퐿= 0, then |훤푖푛| = |S11|. Further, if the |S11| is less than unity that is |S11| < 1, then the region of the output stability circle including the centre of the smith chart is the “stable region” and the second region is the unstable region.

.

The equations for output stability circle in the 훤퐿 plane can be written as follows,

Where,

CL = centre of stability circle

RL = radius of stability circle

Δ = determinant of s-matrix

Δ = 0.275

2 2 DL = (0.488) - (0.275)

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DL = 0.45

CL = (0.488 ˪ 106.8°) - (0.275 ˪ 5.73°) × (0.732 ˪ 64.5°)/0.45

CL = (0.488 ˪ 106.8°) – (0.201 ˪ -70.2°)/0.45

CL = (0.688 ˪ -126.6°)/0.45

CL = 2.1 ˪ -126.6°

RL = (0.221 ˪ -91.0°) × (0.963 ˪ -176.4°)/ 0.45

RL = 1.3

The output stability circle is plotted on the smith chart using above values.

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Figure 3.3: Plot of stability circle on smith chart

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3.5: Selecting value of 휞푻

The following values are obtained from the unstable region in the smith chart.

횪퐓 횪퐢퐧 퐙퐢퐧

0.98˪-100° 0.97˪-43.3° 0.0904-j2.52

0.99˪-102° 1.0˪-44.0° -0.0007-j2.47

0.93˪-104° 0.98˪-46.87° 0.0526-j2.3

0.97˪-104° 1.01˪-45.78° -0.0202-j2.36

0.98˪-106° 1.02˪-46.70° -0.088-j2.31

0.98˪-108° 1.04˪-47.95° -0.12-2.2j

0.98˪-110° 1.05˪-49.23° -0.15-j2.17

0.98˪-112° 1.06˪-50.54° -0.17-j2.10

0.98˪-124° 1.09˪-58.29° -0.18-j1.77

0.98˪-136° 1.06˪-64.72° -0.10-j1.5

0.98˪-154° 0.98˪-71.07° -0.0176-j1.4

Table 3.5.1: Selection of ΓT

The ΓT points are randomly selected from the unstable region in the smith chart. The ΓT values in the circle are selected such that the Γin value obtained is maximum or greater than 1. From the above table, ΓT = 0.98˪-124° is selected since it gives maximum, that is Γin = 1.09˪-58.29°.

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In negative resistance oscillator design, the value of negative resistance should be selected as large as possible. Thus, ΓT value is selected such that it gives maximum Γin which gives greater Zin.

ΓT = 0.98˪-124° lead to

Γin = 1.09˪-58.29°

And ZT = 0.6-j26.6

Thus, for plotting value of Γin on smith chart we take,

1 ∗ = 0.91˪-58.3° Γin

Calculating input port impedance theoretically,

1+ 0.91˪−58.3° = 1− 0.91˪−58.3°

Zin = -0.19-j1.77

Plotting Γin on smith chart to obtain Zin,

Zin = -0.21-j1.77

Parameter Theoretical Smith chart MATLAB

Zin -0.19-j1.77 -0.21-j1.77 -0.18-j1.77

Table 3.6.1: Value of Zin

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The impedance value of generator tuning network can be calculated as,

Zin = -0.18-j1.77

= 9.1/3

= 3.03

= 89j

The value of Rg = 3.03Ω should be give an adequate negative resistance at start-up for successful oscillation.

Zg = Rg + Xg

Zg = 3.03 + j89 Ω

(Zg )푁 = 0.06 + j1.78

Thus, based on the values of Zg and ZT , the generator tuning network can be obtained.

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3.7: Generator Tuning Network Design

For designing generator tuning network, the normalized impedance value (Zg )푁 = 0.06 + j1.78 is plotted on the smith chart.

Figure 3.4: Generator tuning network plotted on smith chart

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From the above smith chart, point A indicates the resistance value which is 3 Ω, used to achieve the resistive component of the generator tuning network impedance. To match a network a short shunt stub is used till point B, whose length is calculated as shown below,

lAB = 0.01λ

To travel from point B to point G, a transmission line is required whose length is calculated as shown below,

lBG = 0.168λ – 0.01λ lBG = 0.158λ

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3.8: Terminating Tuning Network Design

Figure 3.5: Terminating tuning network plotted on smith chart

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From the above smith chart, point A indicates the resistance value which is 50 Ω, used to achieve the resistive component of the generator tuning network impedance. To match a network a short shunt stub is used till point B, whose length is calculated as shown below,

lAB = 0.02λ

To travel from point B to point T, a transmission line is required whose length is calculated as shown below,

lBT = 0.424λ – 0.02λ lBT = 0.404λ

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Figure 3.6: Circuit diagram

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3.9: Microstrip Line Design

A conductor of width w is fabricated on thin grounded dielectric substrate of height h and relative permittivity εr. Since it is an open structure for transmission line, it does not confine for all electric and magnetic fields. Thus, microstrip line cannot support only TEM wave propagation, but support a quasi-TEM mode of propagation. Such a transmission lines are popular and are used in many microwave planar circuit design and microwave integrated technology.

The use of printed circuit board technology and its simplicity of fabrication, with the ease of interconnection of lumped elements and components made this transmission line very popular than other types of planar transmission line. A sketch of electric and magnetic fields is shown below,

Figure 3.8: Electric and magnetic field lines

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Specifications:

f = 16 GHz

Z0 = 50 Ω

εr = 3.6 (Rogers corporation appendix E) h = 0.13 mm (Rogers corporation appendix E) c = 3 × 10^8 m/s

λ0 = c/f

λ0 = 18.8 mm

Calculations:

The transmission line is designed using the following empirical formulas,

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Consider w/h > 2,

From formula, B = 6.2

Thus, w/h = 2.2 h = 0.13 mm

Therefore, w = 0.29 mm

The effective dielectric constant of a microstrip line is given approximately by,

εff = 2.8

The wavelength is given by following formula,

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Using formula for w/h > 0.6

λ = 0.59 λ0

λ = 0.59 × 0.18mm

λ = 11 mm

Calculation of length using direct method:

 Lengths for the generator network,

Shunt stub length: l = 0.01 × 11 = 0.11 mm

Transmission line: l = 0.158 × 11 = 1.738 mm

 Lengths for the terminating network,

Shunt stub length: l = 0.02 × 11 = 0.22 mm

Transmission line: l = 0.404 × 11 = 4.44 mm

Calculation of cut -off frequency (f0),

Where, h in centimetres f0 = 14.65 GHz.

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Microstrip line design result table:

Parameters Hand calculation MATLAB results

λ0 (mm) 18.8 18.7

w/h 2.2 2.2

h (mm) 0.13 0.13

w (mm) 0.29 0.28

εff 2.8 2.81

λ (mm) (50Ω) 11 11.2

f0 (GHz) 14.65 14.65

Table 3.9.1: Microstrip line results

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Figure 3.9: Layout of the circuit

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Chapter 4: AWR Microwave Office

Figure 4.1: Circuit Layout

Figure 4.2: |S21| graph

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Chapter 5: Summary

5.1: Conclusion

In this project, a negative resistance oscillator is successfully designed and implemented using distributed elements technique. For this project, a BJT NPN silicon high frequency transistor is used operating at a frequency of 16 GHz. The stability of the transistor is checked by doing hand calculation and using MATLAB. All the results are verified using CD ROM software (reference 1).

For oscillator design, the generator and tuning matching network are designed using smith chart and the design is verified by performing hand calculations and using MATLAB. Since, transistor operates at 16 GHz, a distributed elements technique is used to design an oscillator. The circuit is simulated in Microwave Office software. The obtained results show an output power greater than 1 dBm at an operating frequency of 16 GHz, which means the circuit will oscillate. Thus, the oscillation conditions are verified.

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The following table indicates the values of the parameters obtained using different calculation methods:

Parameter Hand calculation MATLAB RF/Microwave E-book (Reference1)

k 0.71 0.709 0.71

CL 2.1˪-126.6° 2.13˪-126.6° 2.14˪-126.99°

RL 1.3 1.31 1.31

ΓT 0.98˪-124° 0.98˪-124° 0.98˪-124.0°

Γin 1.08˪-58.1° 1.06˪-64.72° 1.09˪-58.3°

ZT 0.6-j26.6 0.56-j25.4 0.6-j26.6

Zin -0.19-j1.77 -0.18-j1.77 -0.18-j1.78

Zg 0.063+j1.78 0.06-j1.78 0.06+j1.78

Table 5.1: Summary of results

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1. Matthew M. Radmanesh, “Advanced RF & Microwave Circuit Design”, The Ultimate Guide to Superior Design, AuthorHouse, 2009. (RF/Microwave E-book)

2. David M. Pozar, Microwave Engineering (4th ed.). Hoboken, NJ: John Wiley & Sons, Inc., 2011

3. Gonzalez, G. Microwave Transistor Amplifiers Analysis and Design. Englewood Cliffs, 1984.

4. Matthew M. Radmanesh, "RF and Microwave Design Essentials", Bloomington: AuthorHouse, 2007.

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Appendix A

Circuit design using lumped elements

In the design of microwave circuits, usually lumped elements technique is used. The elements in this design are mostly lossless reactive elements like inductors and capacitors and can be added either in series or parallel in the circuit. For oscillator design, generator and terminating matching network are designed lumped elements. The circuit is designed usually by using the smith chart.

Steps for generator tuning network:

1. Plot the value of Zg on smith chart using the resistance circles.

2. Fix the value of point A to be 3Ω which is the value of Rg.

3. Move on constant resistance circle from point A and add the reactance of jXs to arrive at point B. 4. Since it is travelling upwards on constant resistance circle, the lumped element is a series inductor.

The value of the inductor can be calculated as,

For series L:

Xs = 1.78 (from smith chart) j (1.78) = jωL/50

1.78 = 2π×16G × L/50

L = 0.88 nH

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Figure A1: Generator tuning network (lumped elements)

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Steps for designing terminating tuning network:

1. Plot the value of ZT on smith chart using the resistance circles. 2. Locate point A on the centre of the smith chart having value of 50Ω.

3. To reach point C, first travel on constant conductance circle to add the reactance of jB푃 to arrive at point B.

4. Further, from point B add the reactance of jXs to reach till point C.

Since it is travelling downwards from A to B on constant conductance circle, the lumped element is a shunt capacitor. And from B to C, since it is travelling on resistance circle, the lumped element is a series C.

The value can be calculated as,

For shunt C,

For series C,

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Figure A2: Terminating tuning network (lumped elements)

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Figure A3: Circuit layout (lumped elements)

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Appendix B

CD ROM Output

Oscillator design calculation (Reference 1)

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45

46

Microstrip line design calculation

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Appendix C

MATLAB program for oscillator design

clc; clear all; S11=0.732*exp(j*(-64.5/180)*pi); S21=0.963*exp(j*(-176.4/180)*pi); S12=0.221*exp(j*(-91.0/180)*pi); S22=0.488*exp(j*106.8/180*pi); S11c=conj(S11);

Sa=abs(S11); Sb=abs(S12); Sc=abs(S21); Sd=abs(S22); bc=S12*S21; Sbc=abs(bc);

%stability check delta=(S11*S22)-(S12*S21) d=abs(delta) k=(1-(Sa^2)-(Sd^2)+(d^2))/(2*Sbc)

%calculation for stability circle dl=(Sd^2)-(d^2); Nr=conj(S22-(delta*S11c)); Cl=Nr/dl Rcl=abs(Cl) theta=angle(Cl) R=(S12*S21)/(dl); Rl=abs(R)

%matching circuit design gamma_T=0.98*exp(j*(-136.0/180)*pi) gamma_in=S11+((S12*S21*gamma_T)/(1-(S22*gamma_T))) Rgamma_in=abs(gamma_in) thetagamma_in=angle(gamma_in) thetagdeg=(thetagamma_in*180)/pi

% negative resistance zin=(1+gamma_in)/(1-gamma_in)

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Output

delta = 0.2739 + 0.0278i d = 0.2753 k = 0.7091

Cl = -1.2871 - 1.7089i

Rcl = 2.1393 theta = -2.2163

Rl = 1.3107 gamma_T = -0.7050 - 0.6808i gamma_in = 0.4544 - 0.9625i

Rgamma_in = 1.0643 thetagamma_in = -1.1297 thetagdeg = -64.7270 zin = -0.1885 - 1.7726i

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Appendix D

MATLAB program for microstrip line design

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Output

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