现代无线应用高频振荡器设计详解与优化

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现代无线应用中的微波振荡器设计是电子工程领域的一个重要课题，特别是在射频通信、雷达和无线传感器网络等技术中起着至关重要的作用。此文档深入探讨了低相位噪声（Low Phase Noise, LPN）平面集成振荡器的设计理论和优化方法。作者们，Ulrich L. Rohde、Ajay K. Poddar 和 Georg Böck，来自 Synergy Microwave Corporation 和 Technische Universität Berlin，共同撰写了这部专著，旨在为读者提供一个全面且实用的入门指南。在设计现代微波振荡器时，首先要理解基本原理。振荡器的核心是通过正反馈机制将信号放大并维持在一个稳定的频率上。对于无线应用而言，低相位噪声至关重要，因为它直接影响到接收机的性能，如信号的稳定性和灵敏度。低相位噪声意味着信号的随机变化较小，有利于提高通信质量，尤其是在高速数据传输和高精度测量中。文档中详细介绍了几种关键设计策略，包括但不限于： 1. **选择合适的器件**：振荡器设计通常涉及晶体管、电阻、电容和匹配网络的选择，这些器件的特性会影响振荡器的稳定性与噪声水平。设计师需考虑材料特性、温度稳定性以及制造工艺等因素。 2. **电路结构优化**：通过优化电路布局和拓扑，例如使用LC振荡器、石英晶体振荡器或微机械振荡器，可以降低噪声源并提高频率稳定度。 3. **噪声源分析与抑制**：了解并控制可能的噪声源，如热噪声、散弹噪声、电流调制噪声等，是降低相位噪声的关键。这可能涉及到噪声温度的管理、滤波器的设计以及噪声系数的计算。 4. **电源管理**：良好的电源设计和去耦策略对振荡器的性能有重大影响。稳压电源和电源滤波有助于减少电压波动，从而减小噪声。 5. **模拟与数字技术结合**：现代振荡器设计可能融合了模拟和数字技术，如使用数字锁定相环（DLL）来跟踪和校准振荡器频率，确保其长期稳定。 6. **仿真与测试**：使用高级设计软件，如ADS（Advanced Design System），进行模拟仿真，可以帮助工程师预测和优化设计性能。同时，严格的测试流程必不可少，以验证振荡器的实际性能是否达到预期。 "现代微波振荡器设计用于无线应用"文档为读者提供了深入了解这一领域的实用工具和理论基础，不仅涵盖了振荡器设计的基本概念，还强调了在实际应用中如何实现低相位噪声的技巧和策略。无论你是初学者还是资深工程师，这部作品都将为你提供宝贵的知识和指导，推动无线通信技术的发展。

conditions, are not known. Other classic papers, such as that of Kurokawa [82],

indicate where the operating point for the best phase noise lies, but the value of

the phase noise as such is not known [17]. The next breakthrough in oscillator

noise analysis came from Rizzoli et al. [77–79]. It is based on a noise corr elation

matrix and incorporates the various noise sources from the active device. Commer-

cial simulation programs use a ﬁxed topology for the transistor models. Available are

the Gummel-Poon bipolar transistor model, an heterojunction bipolar transistor

(HBT) model, and the various gallium arsenide ﬁeld-effect transistor (FET)-based

models, as well as metal oxide semiconductor (MOS) and JFET models. The

implementation of the noise sources for these semiconductor devices is shown in

the user’s manual of the simulator, speciﬁcally the model library.

The latest approach is a general noise theory for arbitrary circuits, as shown by

Lee et al. [64 – 67]. Their noise model is based on the time-varying properties of

the current waveform of the oscillator, and the phase noise analysis is based on

the effect of noise impulse on a periodic signal.

If an impulse is injected into the tuned circuit at the peak of the signal, it will

cause maximum amplitude modulation and no phase modulation. If an impulse is

injected at the zero crossing of the signal, there will be no amplitude modulation

but maximum phase modulation. If noise impulses are injected between zero cross-

ing and the peak, there will be components of both phase and amplitude modulation.

Based on this theory and the intention to obtain the best phase noise, a special tech-

nique has to be adopted to make sure that any noise impul se occurs at the peak of the

output voltage rather than at any other point. Lee and Hajimiri introduced an impulse

sensitivity function (ISF), which is different for each oscillator topology. This ISF is

a dimensionless function periodic in 2p. It has the largest value whe n maximum

phase modulation occurs and has the smallest value when only amplitude modu-

lation occurs.

This approach appears to be purely mathematical and lacks practicality. The cal-

culation of the ISF is tedious and depends upon the oscillat or topology. The ﬂicker

noise conversion is not clearly deﬁned. Also, there is no general mathematical

equation that can be written for the phase noise in terms of components of the

circuit, which can be differentiated to obtain both maximum power and best nois e

performance. Recent publications by Tom Lee have shown that the noise analysis

for a given topology can be expressed and gives good results once all the data are

known, but it does not lead to exact design rules [107]. Similar to the Leeson

equation, it suffers from the fact that the actual noise performance of the device,

the loaded Q, and the output power are not known a priori. As a matter of fact,

some of the published oscillators by Lee and Hajimiri could be “optimized.” This

means that the published oscillator circuit did not have the best possible phase

noise. By using the optimizer of a commercial harmonic-balance program, the

phase noise could be improved signiﬁcantly. Of course, a good direct synthesis pro-

cedure would have given the correct answer immediately.

The oscillators considered in this work are based on commercially available

silicon bipolar transistors and silicon germanium transistors. As most designers

and companies do not have elaborate and expensive equipment for parameter

INTRODUCTION 3

extraction (to obtain accurate nonlinear models), the design process relies on using

available data from the manufac turer, as well as measurements of large-signal

S-parameters using a network analyzer. Modern microwave transistors are very

well characterized by the manufacturer up to approximately 6 GHz. Noise data, as

well as SPICE-type Gummel-Poon model data sets, are available.

At present, a number of topologies exist that can be used for designing oscillators.

For the purpose of validating the general synthesis procedure, initially, a simple

transistor circuit (Colpitts/Clapp osci llator) is used as the basis of discussion

[2–8]. In Chapter 2, the history of microwave oscillators shows that several

circuit conﬁgurations are possible, and by rotating the circuit, others can be

obtained. A particula rly useful derivative of the Colpitts oscillator is the Meissen

oscillator, which in VCO conﬁgurations has a better phase noise. All other oscillator

conﬁgurations, including VCOs, are a derivative of this basic Colpitts oscillator. The

only exception to this is an oscillator with an inductor in the base. While it can also

be obtained from rotating the grounding point, its basic advantage is a wider tuning

range at the expense of phase noise. All mathemat ical derivations also apply to the

other conﬁgurations.

Using various resonators, we will show that a coupled resonator, rather than a

single resonator, vastly improves the phase noise. The oscillator itself can be

described as a one-port device supplying a negative resistance to the tuned

circuit, which is ideal to determine the best feedback network. Alternatively, it

can be described as a two-port device using a resonator and an ampliﬁer, and

allows us to calculate the complete noise analysis. It will be shown that both

cases provide the same answer. The secon d case gives more insight into the phase

noise calculation. For the ﬁrst time, this new mathematical approach will show a

step-by-step procedure using large-signal conditions for designing an oscillator

with good output power (high efﬁciency) and phase noise. As a third case, the

values for P

out

, Q

, and F required for the Leeson equation will be numerically deter-

mined. All three cases give excellent agreement with the oscillator built under these

test conditions and its measurements. Starting with the simple oscillator, a more

complex circuit, including all the parasitics, will be used to show the general validity

of this approach (Appendix C).

Due to the use of multiple rather than single resonators (since the resonators are

less than quarter wave long, coupled inductors should be used), this book has been

broken down into two sections (1– 9). One concerns the single-resonator case, which

is used to show the systematic approach of noise optimization in general, while

Chapters 10 and 11 are covering multiple resonators, coupled inductors, and

coupled oscillators.

Any successful design for microwave oscillators mandates, besides building and

measuring it, the use and validation with a microwave harmonic-balance simulator.

In the harmonic-balance analysis method, there are two techniques in use to convert

between the time-domain nonlinear model and the frequency-domain evaluation of

the harmonic currents of the linear network. One technique is the almost periodic

discrete Fourier transform technique (APDFT), and the other is the multi-

dimensional fast Fourier transf orm techniq ue (MFFT) using quasi-analytic or

4 INTRODUCTION

analytic derivatives to evaluate the Jacobian matrix. The ﬁrst, which has a somewhat

random sampling approach, has a typical dynamic range of 75– 80 dB, while the

second offers a dynamic range exceeding 180 dB.

In mixer designs and intermodulation analysis, which includes the calculation of

noise in oscillator circuits, it is important to be able to accurately predict a small

signal in the presence of a large signal. To reliably predict this, the dynamic

range (the ratio of a large signal to a minimally detectable small signal) needs to

be more than 175 dB. The APDFT technique was found to have a dynamic range

of 75 dB, while the MFFT, with analytically calculated derivatives, was found to

have a ﬁnal dynamic range of 190 dB. Given the fact that in noise calculations

for oscillators a noise ﬂoor of 2 174 dBm/Hz is the lower reference and the refer-

ence level can be as high as þ20 dBm, a dynamic range of up to 190 dB is required.

Therefore, a numerically stable approach is deﬁnitely required [10 –13].

1.1 ORGANIZATION

This work is organized into 11 chapters.

Chapter 1, the Introduction, describes the purpose of the work and deﬁnes the

problem.

Chapter 2 deﬁnes the oscillator, its application, and parameters. In addition, the

history of microwave oscillators is brieﬂy discussed and various types of oscillators

are introduced.

Chapter 3 describes the various transistor models and gives insight into their par-

ameters. For better understanding, examples of current models are shown.

Chapter 4 develops the concept of large-signal S parameters. The transistor

models shown in Chapter 3 are mostly provided in linear form; the large-signal con-

ditions have to be determined from the SPICE-type time-domain signal parameters.

A good way of describing a transistor under large-signal conditions involves the use

of “large-signal S-parameters,” which are introduced here. Examples of measured

S-parameters are shown [18 – 53].

Chapter 5 discusses resonators used for the frequency-selective circuit of the

oscillator. The popular resonators are shown and resulting Q factors are discussed.

Chapter 6 presents a comprehensive treatment of the oscillator. Initially, the

linear theo ry is shown, which explains the design strategy. Two types of oscillator

conﬁgurations are relevant. One is the parallel type and the other is the series type.

For both cases, a numerical design is shown. The more precise design method of an

oscillator is an approach which considers large-signal conditions. Therefore, the

start-up conditions are described, followed by the steady-state behavior. Under

large-signal conditions, the time-domain behavior has to be considered, as the col-

lector (or drain) current now consists of a DC component and harmonically related

RF currents. In order to describ e this, a normalized drive level is introduced which

determines the conducting angle. As the conducting angle becomes narrower, the

efﬁciency increases and the noise improves. However, there is a wide range over

which the output power is constant but the noise varies widely. Finding the

1.1 ORGANIZATION 5

optimum condition is the objective of Chapter 8. This chapter is supported by

Appendix A.

Chapter 7 provides a detailed discussion of nois e in oscillators, both linear and

nonlinear. For the linear case, the Leeson model is derived, which is used as the

best case model; aproaches to calculate it are presented. It contains the loaded Q,

the noise factor, and the output power. These three variables determine the phase

noise of an oscillator. The linear example is now useful because these three

values are practically unknown. An accurate calculation based on large-signal

S-parameters, speciﬁcally S

, is possible for the ﬁrst time. Finally, a phase noise

test setup is shown which is used to validate this large-sig nal noise theory. This

chapter is supported by Appendix B.

Chapter 8 is the key cont ribution of this monograph. Chapter 6 provides good

insight into the large-signal operation of the oscillator, including its optimization

for power, and discusses some phase noise results under these conditions. As men-

tioned, the normalized drive level x can vary over a broad range, with output powers

only changing a few decibels, while the phase noise changes drastically. A change

in a few decibels of the output power drastically changes the efﬁciency, but the goal

here is to ﬁnd the best phase noise condition. After showing that reducing the

conducting angle and proving that the phase noise improves, the actual noise

calculation and termination of the feedback capacitance is shown. Three cases

are consider ed here:

1. First is the Leeson equation, which contains a need for output power, operat-

ing noise ﬁgure, and testing of the loaded Q for its validity. To do this, the

exact calculations for the outpu t power, the loaded Q, and the resulting

noise factor are presented. An example shows that the accuracy of this

approach is limited, however, since an ideal transistor without parasitics is

assumed.

2. The second approach calculates the noise contribution of a time-varying nega-

tive resistance that cancels the losses. It will be shown that this is a time

average value, that the noise calculations can be further improved, and that

the optimum feedback conditions are found.

3. The third and ﬁnal approach is based on the loop appro ach and considers all

noise contributions. Therefore, it is the most accurate way to determine the

oscillator’s performance. A graphical differentiation of the phase noise

equation shows a point to obtain the best phase noise. The phase noise

increases on either side of this optimal point.

Appendix C shows a complete approach to the design.

Chapter 9 shows ﬁve selected microwave oscillators for validation purposes

which provide state-of-the-art phase noise. Their design was based upon the optim-

ization shown in Chapter 8. Bipolar transistors and gallium arsenide (GaAs) FETs

are used. Measured data were available for the 1000 and 4100 MHz oscillators

with bipolar transistors and for the 2000 MHz GaAs FET oscillator. The ceramic

6 INTRODUCTION

resonator-based oscillator shows a measured phase noise of 125 dBc/Hz at 10 kHz,

145 dBc/Hz at 100 kHz, and 160 dBc/Hz or better at 1 MHz. The 4.1 GHz oscillator

shows a phase noise above 89 dBc/Hz at 10 kHz, 113 dBc/Hz at 100 kHz, and

130 dBc/Hz at 1 MHz, and these results are in excellent agreement with the predic-

tion. Due to its high ﬂicker corne r frequency, the GaAs FET may cause modeling pro-

blems. The fourth example is a 77 GHz oscillator based on published information, in

which the design, the simulation, and the measurements agree well. The ﬁfth, and

last, example is based on a wide microstrip resonator, which requires electromagnetic

tools for simulation. This case shows the design items necessary for such an

oscillator.

The previous chapters deal with single-resonator design. In Chapter 10, we will

introduce a system of coupled oscillators and a multiple-resonator approach. This

gives far better results than a single oscillator, but the level of effort is also much

higher. This chapter describes both the coupling and locking mechanisms, as well

as the noise analysis applicable for these cases. Also of particular interest is the

wideband VCO, which is described at the end of this chapter. In particular, the

design criteria for this oscillator are covered in great detail, including the inﬂuence

of the components.

Chapter 11 shows validation circuits for multiple-coupled resonator-based and

multiple-coupled oscillators; speciﬁcally, the case of the VCOs is shown. Both

design information and results are given. This hybrid-tuned ultra-low-noise wide-

band VCO has set the state of the art and is a result of many techniques covered

in this book.

The book ends with Appendices A to H, which contain three oscillator designs.

The appendices are very important because they apply all the design rules presented

in this monograph. The chosen circuits were also used for veriﬁcation purposes.

Appendix A describes the oscillator design using large-signal S-parameters for

optimum power. The unique approach used here also shows that an inductor,

instead of a feedback capacitor, may be needed to make the design for a given tran-

sistor possible. This has not been shown in the literature before.

Appendix B describes the Bessel functions in a large-signal design for best output

power. Consistent with Appendix A, a detailed numerical approach is given so that

the step-by-step procedure can be easily followed. Again, the design is a typical

application for a high-performance oscillator. In this case, the output power was

the priority and the phase noise was allowed to degrade.

Appendix C combines all the technologies discussed in this monograph to show

the optimum design of oscillators. It starts with the speciﬁc requirements for output

power and phase noise. It further assumes a real transistor with its parasitics con-

sidered. It shows the schematic ﬁrst, which is the optimum choice for this appli-

cation. The Bessel function approach is used to determ ine the operating point and

the bias point. The design calculation shows that the key equation (8-94) in

Chapter 8, despite its simpliﬁcation, gives an accurate answer for the phase noise.

The result is consistent with the predicted phase noise, predicted by the equation

derived here, the predicted values using Ansoft’s harmonic balanced simulator

designer, and the measured phase noise.

1.1 ORGANIZATION 7

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