Fundamentals of RF Circuit Design with Low Noise Oscillators Jeremy Everard Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-49793-2 (Hardback); 0-470-84175-3 (Electronic) Low Noise Oscillators 4.1 Introduction The oscillator in communication and measurement systems, be they radio, coaxial cable, microwave, satellite, radar or optical fibre, defines the reference signal onto which modulation is coded and later demodulated The flicker and phase noise in such oscillators are central in setting the ultimate systems performance limits of modern communications, radar and timing systems These oscillators are therefore required to be of the highest quality for the particular application as they provide the reference for data modulation and demodulation The chapter describes to a large extent a linear theory for low noise oscillators and shows which parameters explicitly affect the noise performance From these analyses equations are produced which accurately describe oscillator performance usually to within to 2dB of the theory It will show that there are optimum coupling coefficients between the resonator and the amplifier to obtain low noise and that this optimum is dependent on the definitions of the oscillator parameters The factors covered are: The noise figure (and also source impedance seen by the amplifier) The unloaded Q, the resonator coupling coefficient and hence QL/Q0 and closed loop gain The effect of coupling power out of the oscillator The loop amplifier input and output impedances and definitions of power in the oscillator Tuning effects including the varactor Q and loss resistance, and the coupling coefficient of the varactor The open loop phase shift error prior to loop closure 180 Fundamentals of RF Circuit Design Optimisation of parameters using a linear analytical theory is of course much easier than non-linear theories The chapter then includes eight design examples which use inductor/capacitor, surface acoustic wave (SAW), transmission line, helical and dielectric resonators at 100MHz, 262MHz, 900MHz, 1800MHz and 7.6GHz These oscillator designs show very close correlation with the theory usually within 2dB of the predicted minimum The Chapter also includes a detailed design example The chapter then goes on to describe the four techniques currently available for flicker noise measurement and reduction including the latest techniques developed by the author’s research group in September 2000, in which a feedforward amplifier is used to suppress the flicker noise in a microwave GaAs based oscillator by 20dB The theory in this chapter accurately describes the noise performance of this oscillator within the thermal noise regime to within ½ to 1dB of the predicted minimum A brief introduction to a method for breaking the loop at any point, thus enabling non-linear computer aided analysis of oscillating (autonomous) systems is described This enables prediction of the biasing, output power and harmonic spectrum 4.2 Oscillator Noise Theories The model chosen to analyse an oscillator is extremely important It should be simple, to enable physical insight, and at the same time include all the important parameters For this reason both equivalent circuit and block diagram models are presented here Each model can produce different results as well as improving the understanding of the basic model The analysis will start with an equivalent circuit model, which allows easy analysis and is a general extension of the model originally used by the author to design high efficiency oscillators [2] This was an extension of the work of Parker who was the first to discuss noise minima in oscillators in a paper on surface acoustic wave oscillators [1] Two definitions of power are used which produce different optima These are PRF (the power dissipated in the source, load and resonator loss resistance) and the power available at the output PAVO which is the maximum power available from the output of the amplifier which would be produced into a matched load It is important to consider both definitions The use of PAVO suggests further optima (that the source and load impedance should be the same), which is incorrect and does not enable the design of highly power efficient low phase noise designs which inherently require low (zero) output impedance The general equivalent circuit model is then modified to model a high efficiency oscillator by allowing the output impedance to drop to zero This has recently been used to design highly efficient low noise oscillators at L band [6] which demonstrate very close correlation with the theory Low Noise Oscillators 4.3 181 Equivalent Circuit Model The first model is shown in Figure 4.1 and consists of an amplifier with two inputs with equal input impedance, one to model noise (VIN2) and one as part of the feedback resonator (VIN1) In a practical circuit the amplifier would have a single input, but the two inputs are used here to enable the noise input and feedback path to be modelled separately The signals on the two inputs are therefore added together The amplifier model also has an output impedance (ROUT) The feedback resonator is modelled as a series inductor capacitor circuit with an equivalent loss resistance RLOSS which defines the unloaded Q (Qo) of the resonator as ωL/RLOSS Any impedance transformations are incorporated into the model by modifying the LCR ratios The operation of the oscillator can best be understood by injecting white noise at input VIN2 and calculating the transfer function while incorporating the usual boundary condition of Gβ0 =1 where G is the limited gain of the amplifier when the loop is closed and β0 is the feedback coefficient at resonance V IN (n oise) R IN R OUT V IN R IN (F eedba ck ) C R LO SS L Figure 4.1 Equivalent circuit model of oscillator The noise voltage VIN2 is added at the input of the amplifier and is dependent on the input impedance of the amplifier, the source resistance presented to the input of the amplifier and the noise figure of the amplifier In this analysis, the noise figure under operating conditions, which takes into account all these parameters, is defined as F The circuit configuration is very similar to an operational amplifier feedback circuit and therefore the voltage transfer characteristic can be derived in a similar way Then: 182 Fundamentals of RF Circuit Design VOUT = G (VIN + VIN ) = G (VIN + βVOUT ) (4.1) where G is the voltage gain of the amplifier between nodes and 1, β is the voltage feedback coefficient between nodes and and VIN2 is the input noise voltage The voltage transfer characteristic is therefore: VOUT G = VIN − ( βG ) (4.2) By considering the feedback element between nodes and 2, the feedback coefficient is derived as: β= RLOSS + RIN R IN + j (ωL − / ωC ) (4.3) Where ω is the angular frequency Assuming that: ∆ω