BJT Noise Models

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Chapter 2 Basic Oscillator Design

In this chapter, the basic method of oscillator design will be discussed. Some consider basic oscillator design to be somewhat of an art [13]. However, using the nonlinear techniques of Clarke and Hess [5], and the three-terminal model from Davis [6], the process of designing an oscillator can be fairly straightforward. We will start off with a basic description of an oscillator. We will then proceed to discuss the nonlinear sources that can be used to model the device used in an oscillator. The exponential source will be discussed in more detail because it can be used to model the Bipolar Junction Transistor (BJT). The BJT will be used throughout the thesis in examples; however, the concepts discussed can be applied to other devices. After discussing the nonlinear source, the three-terminal oscillator model is discussed. This allows for a short discussion on oscillator design and the effects of saturation on a design.

Basic Oscillator Description

One way to view an oscillator is as an active device with positive frequency dependent feedback. Figure 2.1 shows a diagram of this simplified model. Thermal noise and startup transients start the oscillation by providing a wide-band signal at the input of the active device. The positive feedback path is generally a frequency selective circuit, which filters the output of the active device and adds to the input signal at the desired frequency of oscillation. As this process of amplifying wide-band noise and feeding back the filtered output of the active device is repeated, a signal at the fundamental frequency emerges from the noise. The emerging oscillation continues to increase to the point where it is limited by some nonlinear characteristic of the active device or an automatic gain control circuit.

Nonlinear Sources

The active device of an oscillator is generally a nonlinear device which produce currents as a result of an input voltage. A large signal analysis must be used to relate the input voltage to the output current. A sinusoidal input voltage will produce currents at the fundamental frequency and some harmonics, depending on the device. The nonlinear properties of the device can also shift the bias point depending on the amplitude of the driving voltage. The techniques used here can be used for any nonlinear characteristic. For the purposes of this thesis, we will focus on the exponential characteristic of the bipolar junction transistor (BJT). To see details of the analysis of circuits with other characteristics such as piecewise linear, square law, or differential, please refer to Chapter 4 of Clarke and Hess [5].where kTq is approximated by 26 mV at a temperature of 300 K [5]. The V-I relationship for the exponential characteristic is illustrated in Figure 2.2. For the purpose of an oscillator we may assume the base-emitter voltage is sinusoidal. This gives us where x = qV1 kT . As the drive, x, is increased, a sharper current pulse with a lower duty cycle is created, which can be seen in Figure 2.3. For the large signal analysis of an oscillator, we would like to know the harmonic content of the current in the transistor. Since e x cos(wot) is periodic, the emitter current can be represented as a Fourier Series of the form.

Three-Terminal Model

The three-terminal model method of oscillator design is a simple way of representing the feedback and active device in an oscillator circuit. This method requires drawing the model of the circuit at the fundamental frequency of oscillation. The tank capacitance and inductance are placed across the appropriate terminals in parallel with any conductances required for biasing. A model for the nonlinear device is then inserted in the circuit, and loop equations for the circuit can now be written. For the purposes of this thesis, a bipolar junction transistor (BJT) will be used for the active device in the oscillator. However, the model can be used for other nonlinear characteristics by using a different nonlinear device model. When using the three-terminal model the common-collector, common-base, and common-emitter configurations all reduce to the same topology. The simplification to the three-terminal model is illustrated in Figure 2.5. A table relating the three-terminal model conductance values to the original circuit components is provided in Table 2.2. The common-collector topology will be used in this thesis. For a BJT operating in a non-saturating environment the α-Model from Davis [6], shown in Figure 2.6, can be used. Once this model is inserted into the three-terminal model, the circuit can be rearranged and loop equations can be derived. Figure 2.7 shows the circuit with the α-model inserted, while Figure 2.8 has been rearranged to facilitate derivation of the loop equations. In Figure 2.8, the load has been represented as if it is included in the transistor model. With the basic case of an oscillator that does not saturate, the load resistance represented in Figure 2.8 is in series with a current source and has no effect on the design

1 Introduction 
2 Basic Oscillator Design 
2.1 Basic Oscillator Description .
2.2 Nonlinear Sources 
2.3 Three-Terminal Model 
2.4 Oscillator Design 
2.5 Effects of Saturation on Design 
3 Example Oscillator Designs 
3.1 Non-Saturating Common-Collector Oscillator Example 
3.2 Saturating Common-Collector Oscillator Example 
3.3 Effects of a Collector Load on Common-Collector Oscillator Performance
4 Noise
4.1 Sources of Noise 
4.1.1 Thermal Noise
4.1.2 Flicker Noise
4.1.3 Partition Noise
4.1.4 Shot Noise
4.2 BJT Noise Models 
4.3 Modification of BJT Noise Model to Include Saturation 
4.4 Computation of In-phase and Quadrature Power 
4.5 I/Q Decomposition of Shot Noise 
4.6 Loop Transfer of Noise 
4.6.1 Device Transfer
4.6.2 Derivation of Loop Transfer for a Non-Saturating Oscillator .
4.6.3 Derivation of Loop Transfer for a Saturating Oscillator
5 Noise Performance of Examples
5.1 Advanced Design System Phase Noise Simulation 
5.2 Non-Saturating Common-Collector Oscillator Example 
5.3 Saturating Common-Collector Oscillator Example 
5.4 Effects of a Collector Load on Common-Collector Oscillator Phase Noise
6 Conclusions and Recommendations 

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