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# Voltage Controlled Oscillators

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Application Notes
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In this application note, let us model some Voltage Controlled Oscillators (VCOs), such as, Dual Integrator VCO and Controlled Reactance VCO, using PSpice. Most of the examples in the application note use the Analog Behavioral Modeling capabilities of PSpice. Most of the examples in the application note use the Analog Behavioral Modeling capabilities of PSpice.

## Dual Integrator VCO

An alternate approach to a behavioral model VCO is to start from a 2-integrator loop. Changing the time constant of one or both integrators allows the frequency of oscillation to be controlled. Some form of limiting is required in order to produce output of bounded amplitude.

A particularly elegant example can be found in Reference. This sinusoidal VCO has independent control of both frequency and amplitude. It's black-box representation reduces to: Figure 1: Black-box representation of a sinusoidal VCO

Outputs `Vd` and `Vo` are in quadrature. The amplitude error term is obtained by squaring and summing the quadrature outputs, and subtracting the amplitude-setting voltage `Va`.

Using the `.FUNC` command, the entire VCO can be reduced to two integrators with controlled current sources whose expressions incorporate the multiplications, additions, and subtractions.

Following is an example to model the above VCO:

* Filanovksy VCO

`.func ve(x,y,z) k*(pwr(x,2)+pwr(y,2)-pwr(z,2)`

`.param k=0.1, cv=10u`

`g1 vd 0 value {k*((-v(vo)*v(vf))+(ve(v(vo),v(vd),v(va))*v(vd)))}`

`c1 vd 0 {cv}`

`r1 vd 0 1G`

`g2 vo 0 value {k*v(vd)*v(vf)}`

`c2 vo 0 {cv}`

`   r2 vo 0 1G`

`.ic v(vd)=0.1, v(vo)=0`

`va va 0 1v`

`vf vf 0 1v` Figure 2: Circuit Design for Filanovsky VCO Figure 3: Simulation results for Filanovsky VCO

## Controlled Reactance VCO

A more circuit oriented approach to build a VCO is to take a simple tank oscillator and use a voltage-dependent reactance for one of the tank components. The following example is a Colpitts oscillator. The zx device is used to implement a voltage-controlled lossy inductor.

xvi ctrl 0 ref vcc c zx;Colpitts with variable tank element,

lref ref ref1 15u

rref ref1 0 2.0

c1 c e 20n

c2 e 0 200n

q1 c 0 e q2n2222

re e vee 2k

vcc vcc 0 10v

vee vee 0 -10v

vctrl ctrl 0 pwl(0,1.5v 124u,1.5v 125u,2.5v)

.ic v(c) = 10 v(e) = -0.7 Figure 4: Circut Design for Controlled Reactance VCO Figure 5 : Simulation results for Controlled Reactance VCO

Reference

 I. M. Filanovsky, “Sinusoidal VCO with Control of Frequency and Amplitude,” Proceedings of the 32nd Symposium on Circuits and Systems, IEEE, Vol I, 446-449 (1989). 