Voltage Controlled Oscillator
Introduction
One of the components of a PLL is the voltage controlled oscillator (VCO). There are several
ways in which these can be realized; LC

based and ring oscillator based. In this report we
consider the LC

based osc
illator.
An excellent reference is [1].
LC Oscillator
Every LC oscillator has an inductance and capacitance connected to an active circuit. The role of
the active circuit is to provide a negative resistance to counterbalance the positive resistance
pre
sent in the passive LC circuit. The purpose of the LC circuit is to determine the frequency of
oscillation.
We model the LC oscillator as shown in Figure 1.
Figure
1
Oscillator Model R =

R1 is the input resistance of the active circuit.
We convert this to discrete form in the usual way, using the transformation from the
s

plane to the z

plane s

> (z
–
1)/T, where T is the sample rate of the digital system.
The equations are as follows.
For R = 0
Th
e last equation for
,
I
,
has
poles
on the unit ci
rcle with the position of the po
les
determined by the equation
fo
r the cosine.
This determines the frequency of oscillation.
These equations
can now easily be programmed in Simulink using the SPO blocks.
Figure 2 shows the
Simulink Model.
Figure 2 Simulink Model
theta
Running this model shows the expected oscillation.
Figure 3 Circuit Response
Analysis
The next step is to analyze the performance of this circuit in terms
of the parameters important to
its use in a PLL. These include frequency stability, phase noise, amplitude noise and others as
discussed in [1].
Matlab has many tools to perform such analyses. For example it is
easy
to compute the FFT of
the oscillator
output to determine the spectral purity.
Figure
4 shows
the FTT of a wave with
32768 points.
Figure 4 FFT of Oscillator Signal, Overall and Detail
Oscillator
Notes
The MDL file is ibmvco2.mdl In IBM
The evaluation program is
ff = a
bs(fft(simout)); stem(ff,'.'); zoom xon
The plan is to study the performance of the oscillator with respect to noise and other
factors.
References
[1] “High Purity Oscullators”, E Hegazi, J Rael, A Abidi, Kluwer, 2005
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