GaAs 2000 – Paris, France 2-6 October 2000
Abstract Microwave oscillator design is based on the principle of generating a negative resistance to compensate for the losses of the resonator. Several circuit combinations, including one- and twoport oscillators, are possible. In this discussion, we will first evaluate the conditions of oscillation for the Colpitts and Clapp-Gouriet oscillator. We will then evaluate a 19-GHz SiGe-based oscillator by assuming values, backed up by available S parameters and dc I-V curves, that we assigned to the nonlinear BFP520 model. So far it has been difficult to obtain complete documentation on modeling for the SiGe transistors, but our approximation appears to be justified. Next, we will evaluate a ceramic-resonator-based oscillator and show its performance. Going up to higher frequencies, we will introduce a 47-GHz lumped-resonator oscillator and a VCO at the same frequency that uses GaAsFETs as varactors. In all cases, we will give a thorough treatment of the circuits and their performance. Introduction This presentation will give an overview of both bipolar and GaAsFET-based oscillators, including ceramic-resonator oscillators (CROs). Its purpose is to show not only the linear/nonlinear mathematics, but also how the actual design should be considered, as well as commentary on the results. Many of the predictions can only be obtained by using appropriate software; for this purpose, we have used a harmonic-balance simulator by Ansoft. We also will show some practical circuits, both from the circuit design as well as the actual chip design. In the assumptions we have taken, we have avoided shortcuts so that the approach remains general in nature. It further needs to be pointed out that throughout this discussion, we will assume that each oscillator is followed by an isolation stage that can handle the input power, has at least 10 dB of amplification, and provides isolation of more than 30 dB. An FET amplifier is ideal because it will load the oscillator very little. Basic Oscillator Conditions An oscillator is an electronic circuit that overcomes the losses of a resonator by applying energy at the resonator frequency into the resonator. This and the initial switch-on transient will start oscillation, and the oscillator’s amplitude will be limited and stabilize based on the nonlinearities of the active device(s). What really happens is that the transistor will change its dc transconductance at startup condition into a new dc transconductance and a transconductance ∗
Department of Electrical Engineering, Universities of Oradea, Bradford, and George Washington. Copyright 2000 by Ulrich L. Rohde
value for the fundamental frequency and its harmonics. The total sum of these transconductances needs to be the same as the starting value at a given dc point. This is the mechanism that stabilizes the oscillation and creates harmonic content, including a dc level shift that reduces the actual loop gain to exactly 1. The required necessary (negative) resistance to compensate for the losses and enable oscillation is calculated by
(1) Figure 1 shows the voltage divider of the Colpitts oscillator
Figure 1-- Input of a Colpitts oscillator; the capacitive divider generates a negative input resistance which will start oscillation if an inductor is added.
The value of S21 can be obtained from the datasheet and the resulting Rn should be negative and sufficiently large to compensate the losses. On the other hand, there is a limit to how large the capacitance can be made. As the capacitance increases, the magnitude of Rn gets smaller and will no longer be large enough to compensate the losses. To demonstrate this, we have plotted in Figure 2 the real and imaginary values of the input impedance Z11 of Port 1 of the circuit shown in...