Determine the frequency for the Wien-bridge oscillator in Figure 10–12 . Also, calculate the setting for Rf assuming the internal drain-source resistance, rds' , of the JFET is 500 Ω when oscillations are stable.

Question

Determine the frequency for the Wien-bridge oscillator in Figure 10–12 . Also, calculate the setting for [latex]R_f[/latex] assuming the internal drain-source resistance, [latex]r_{d s}^{\prime}[/latex] , of the JFET is 500 Ω when oscillations are stable.

Accepted Answer

For the lead-lag network, [latex]R_1=R_2=R=10 \mathrm{k} \Omega[/latex] and [latex]C_1=C_2=C=0.01 \mu \mathrm{F}[/latex]. The frequency is

[latex]f_r=\frac{1}{2 \pi R C}=\frac{1}{2 \pi(10 \mathrm{k} \Omega)(0.01 \mu \mathrm{F})}=1.59 \mathrm{kHz}[/latex]

The closed-loop gain must be 3.0 for oscillations to be sustained. For an inverting amplifier, the gain is that of a noninverting amplifier.

[latex]A_v=\frac{R_f}{R_i}+1[/latex]

[latex]R_i[/latex] is composed of [latex]R_3[/latex] (the source resistor) and [latex]r_{d s}^{\prime}[/latex] . Substituting,

[latex]A_v=\frac{R_f}{R_3+r_{d s}^{\prime}}+1[/latex]

Rearranging and solving for [latex]R_f[/latex] ,

[latex]R_f=\left(A_v-1\right)\left(R_3+r_{d s}^{\prime}\right)=(3-1)(1.0 \mathrm{k} \Omega+500 \Omega)=3.0 \mathrm{k} \Omega[/latex]

P R A C T I C E EXERCISE*

What happens to the oscillations if the setting of [latex]R_f[/latex] is too high? What happens if the setting is too low?

Question 10.1: Determine the frequency for the Wien-bridge oscillator in Fi...

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