# Analysis of BJT RC Phase Shift Oscillator

I have designed an RC phase shift oscillator and it works in LT spice but i want to know if the analysis i have did on this circuit is correct or not. I want to calculate the "gain" as well as the "input impedance". Please guide me where i am wrong because i am a beginner in electronics. It oscillates at around 500Hz.

• AC analysis

$$\|Z_{in}| = |(X_{C1}||R3)| \approx 315\Omega \$$

$$\|Z_{in_{base}}| = |(R1||R2)||\beta*Z_{in}| \approx 13K\Omega\$$

$$\|Z_{out}|= |Z_{RCnetwork}||R4| \approx 8K \Omega\$$

$$\\text{Voltage Gain} = Z_{out}/Z_{in} \approx 25.4\$$

• DC analysis

$$\ V_{b} = 1.62V \$$ $$\ I_e \approx 0.4mA \$$ $$\ V_c \approx 5V \$$

My questions are -

• Why is there sustained oscillations even when the voltage gain is around 25. Shouldn't the voltage gain be around 29. Where am i wrong in my analysis.Is my AC analysis correct?
• Is my Dc analysis of the circuit correct since i want the signal to swing around the midpoint i.e 4.5V
• You haven't stated what frequency it oscillates at. Commented Mar 25, 2021 at 9:13
• It oscillates at around 500Hz. Sorry i forgot to write it. Commented Mar 25, 2021 at 9:46
• @shahroze shahab, your gain formula is wrong. The gain can be approximated using Zout/RE with emitter resistor R3. However, in your case R3 is bypasssed with a C and there is no signal feedback. Therefore, you must use the correct formula gain Av=-Zout*gm (gm=transconductance=Ic/26mV)
– LvW
Commented Mar 25, 2021 at 10:22
• @Lvw But the oscillations are low at around 500 hz. So the reactance of the capacitor C1 is finite. Shouldn't we take the combined impedance with R3 into account?? Commented Mar 25, 2021 at 10:26
• Oh yes, you are right - for 500 Hz the capacitor C1 has a finite impedance of app. 320 ohms. So your calaculation is OK - I was confused because you wrote "Zin". Therefore, it was not clear to me that you spoke about the emitter leg. Sorry.
– LvW
Commented Mar 25, 2021 at 10:47