Summary: AE_Lecture5_PartA describes the short Circuit Time Constant Method of determining the lower -3dB frequency of RC coupled CE Amplifier.

**AnalogElectronics_Lecture5_PartA_Low Frequency Analysis of CE Amplifier(Final)**

Figure 1. RC-coupled CE Amplifier.

Lower -3dB frequency of CE Amplifier is determined by Short Circuit Time Constant Method.

Coupling Capacitors and Emitter By-pass capacitor are responsible for lower -3dB frequency(f_{L}).

We consider the time constant associated with each capacitor with the remaining capacitors shorted. Suppose the time constants associated with C_{C1}, C_{C2} and C_{E} are τ_{1S }, τ_{2S }and τ_{3S }. Then the overall time constant associated with the amplifier due to combined effect of C_{C1}, C_{C2} and C_{E }is τ_{L} where:

Here Time Constant associated with each capacitor is τ = RC where R is the equivalent resistance seen by each Capacitor.

Figure 2. Low Frequency Incremental model

Figure 3. Low frequency Incremental Model with C_{E} and Cc2 shorted. Equivalent resistance seen by Cc1 is R_{S} + (R_{B}||(r_{x}+r_{π}))

Figure 4. Incremental Model with Cc1 and Cc2 shorted. Ce sees the equivalent Resistance R_{2s}= v_{o}/i_{o}

In Figure 4 , a voltage source v_{o} is connected in place of C_{E} .

Current drawn from the source is : i_{o}= i_{b} + β_{fo}. i_{b}

where i_{b} = v_{o}/(r_{π}+ r_{x}+ R_{B}||R_{S}) therefore i_{o }= i_{b}(1 + β_{fo})= (1 + β_{fo}).v_{o}/(r_{π}+ r_{x}+ R_{B}||R_{S});

Therefore v_{o}/ i_{o} = (r_{π}+ r_{x}+ R_{B}||R_{S})/ (1 + β_{fo})= R_{2s} ;

By detailed analysis,

Here there are two poles corresponding to two capacitors C_{C1} and C_{E} . The second coupling capacitor is considered to be infinity. The highest pole decides lower -3dB frequency. So 0.188Krads/sec decides the lower -3dB frequency which comes out to be 30Hz.