RC Oscillators

RC oscillators use resistors and capacitors, instead of inductors, to generate low-frequency signals. The two important RC oscillators in the II PUC Electronics syllabus are the phase-shift oscillator and the Wein bridge oscillator.

Principle of phase shift in an RC circuit

A phase-shift circuit is simply an RC network. One section (Figure 6.3.1a) has a series capacitor $C$ and a shunt resistor $R$, with input $V_i$ applied and output $V_o$ taken across $R$. When an AC voltage is applied, the voltage across $R$ leads the applied voltage by an angle $\phi$, where

The value of $\phi$ depends on $R$ and $C$: if $R = 0$ then $V_o$ leads $V_i$ by 90 degrees ($\phi = 90^\circ$); if $R = \infty$ then $\phi = 0^\circ$. In practice $R$ is chosen so that each section gives a convenient lead. Three such RC sections in cascade (Figure 6.3.1b), each contributing 60 degrees, produce a total phase shift of 180 degrees, so the network output leads its input by 180 degrees.

Phase-shift oscillator

A phase-shift oscillator (Figure 6.3.2) uses an op-amp as the amplifying stage and three RC sections as the feedback network. The feedback network provides 180 degrees of phase shift and the op-amp inverting amplifier adds a further 180 degrees, so the loop phase shift is 360 degrees — the condition for positive feedback — and the circuit oscillates. Its frequency of oscillation is

At this frequency the required amplifier gain is $A = \dfrac{R_f}{R_i} = 29$ and the feedback fraction is $\beta = \dfrac{1}{29}$ (so that $A\beta = 1$).

Principle of the lead-lag network

A lead-lag network is a circuit whose output voltage leads or lags the input voltage depending on frequency (Figure 6.3.3). It consists of a series combination of R1 and C1 followed by a parallel combination of R2 and C2. At low frequencies the series capacitor C1 behaves like an open circuit, so there is no output; at high frequencies the shunt capacitor C2 behaves like a short circuit, so again there is no output. At one particular frequency $f$ the output is a maximum, and when $R_1 = R_2 = R$ and $C_1 = C_2 = C$,

At low frequencies the phase angle is positive (the circuit leads), at high frequencies it is negative (the circuit lags), and at the frequency $f$ the phase angle is exactly zero. This zero-phase-shift, maximum-output condition is what the Wein bridge oscillator exploits.

Wein bridge oscillator

In the Wein bridge oscillator (Figure 6.3.4) a Wein bridge is connected between the amplifier's input and output terminals. One arm of the bridge is a series R1-C1 network, the adjoining arm is a parallel R2-C2 network, and the remaining two arms carry resistors R4 (= Ri) and R3 (= Rf). The phase criterion is that the total phase shift around the circuit must be 0 degrees, which happens only when the bridge is balanced — that is, at resonance. The frequency of oscillation is

The feedback (bridge) path produces no phase shift. The balance condition of the bridge is

which reduces to $\dfrac{R_3}{R_4} = 2$ when the R's and C's are equal. The op-amp is used as a non-inverting amplifier, so its voltage gain is $A = 1 + \dfrac{R_3}{R_4} = 3$, the feedback fraction is $\beta = \dfrac{1}{3}$, and the closed-loop gain is therefore $A\beta = 1$.

Advantages, disadvantages, applications and limitations

Advantages of RC oscillators: (1) they need no inductors; (2) they can produce audio-range frequencies; (3) good frequency stability; (4) they can be used as variable-frequency oscillators; (5) the circuit is compact and less expensive. …