Cascading transistor amplifiers

When the amplification provided by a single stage amplifier is not  suffiecient for a particular purpose or when the input and output impedance is not of the correct magnituded for the required application then two or more amplifiers are connected in

 cascade as shown below.

             

Here the output of amplifier 1 is connected as the input of amplifier 2.

Example: The gain of a single amplifier is not sufficient to amplify a signal from a weak source such as microphone to a level which is suitablefor the operation of another circuit as loud speaker. In such cases, amplifiers are used.

When amplifiers are cascaded, individual amplifiers provides required amplification and input and output provide impedance matching.

Decibel (dB)

Many  a times it is convenient to represent the gain of an amplifier on a log scale instead of a linear scale. The unit of this log scale is called decibel.

Power gain =log_e( Pout /Pin ) bel

Power gain in dB =10 log₁₀( Pout /Pin ) dB

Voltage gain =20log₁₀( Vout /Vin ) dB

Current gain = 20log₁₀(I_out / I_in ) dB

Note: For a multistage amplifier if A_V1, A_V2, and A_V3 are the voltage gains of amplifier 1,2, and 3 respectively then the overall voltage gain A_V = A_V1 x A_V2 x A_V3.

If it is expressed in dB the A_V(dB) = A_V1(dB) + A_V2(dB) +A_V3(dB)

Similarly for four or more stages.

Single stage RC coupled Amplifier

 

Figure above shows a practical circuit of a single stage RC coupled amplifier.The different circuit components and their functions are as described below.

1. Input capacitor(C_in)- This capacitor is used to couple the input signal to the base of the transistor if it is not used, the signal source resistance R_S gets in parallel with R₂ thus changing the bias. The capacitor C_in blocks any d.c. component present in  the signal and passes only a.c. signal for amplification.

2. Biasing circuit –The resistances R₁, R₂ and R_E forms the biasing and stabilization circuit for the CE amplifier. It sets the proper operating point for the amplifier.

3. Emitter bypass capacitor (C_E)-This capacitor is connected in parallel with the emitter resistance R_E to provide low reactance path to the amplified a.c. signal. If it is not used, the amplified a.c. signal passing through R_E will cause voltage drop across itthereby reducing the output voltage of the amplifier.

4. Coupling capacitor(Cc)- This capacitor couples the output of the amplifier to the load or to the next stage of the amplifier. If it is not used, the biasing conditions of the next stage will change due to the parallel effect of collector resistor R_C.

i.e. R_C will come in parallel with the resistance R₁ of the biasing network of the next stage thus changing the biasing conditions of the next stage amplifier.

Two stage RC coupled amplifier

Figure above shows the circuit diagram of  a two stage RC coupled amplifier . The coupling capacitor C_C connects the output of the first stage to the input of the second stage. Since the coupling from one stage to the next stage is achieved by coupling capacitor along with a shunt resistor the amplifier is called RC coupled amplifier.. The input signal is first applied to the transistor T₁ and output is taken at the collector of T₁. The signal at the output will be 180⁰  out of phase when compared to the input. The output is taken across R_C with the help of a coupling capacitor. This signal is fed as input to the next stage i.e transistor T₂. The signal is amplified further  and the amplified output is taken across R_c¹ of T_2.  The phase of the signal is reversed again. The output is amplified twice and its is amplified replica of the input signal.

 Frequency response in amplifer

Frequency response is the curve between the gain of the amplifier (A = V_o / V_i ) verses the frequency of the input signal. The frequency response of a typical RC-coupled amplifier is shown below.

Frequency response has 3 regions.

1.   Low frequency range

1. Mid frequency range
2. High frequency range

Low frequency range (< 50 Hz)

We have

Since frequency is inversely proportional to the reactance, the reactance of the coupling capacitor C_C will be quite high at low frequencies.

Hence very small amount of signal will pass through one stage to the next stage. Moreover  C_E cannot shunt the emitter resistance R_E effectively because of its large reactance at low frequency. These two factors causes the fall of voltage gain at low frequencies.

Mid frequency range (50Hz –20KHz)

In this range of frequencies, voltage gain of the amplifier is constant. The effect of coupling capacitor in this range is as such to maintain a uniform voltage gain.

High frequency range (> 20 KHz)

 In this range of frequency, the reactance of the coupling capacitor C_C is very small and it behaves as a short circuit.  This increases the loading effect of next stage ( R_C will comes in parallel with R₁) and reduces the voltage gain. This reduces the current amplification there by the voltage drops at high frequencies.

Advantages of RC coupled amplifer

1. Low cost-Because only resistors and capacitors are used for biasing and coupling which are cheap.
2. Compact-Because modern resistor and capacitors are small and light
3. Good frequency response- The gain is constant over the audio frequency range and hence suitable for audio frequency amplification.