Cascade amplifier and R-C coupled ampifier

R-C coupled amplifier:

RC coupled coupling is the most widely used method of coupling in multistage amplifiers. In this case the resistance R is the resistor connected at the collector terminal and the capacitor C is connected in between the amplifiers. It is also called a blocking capacitor, since it will block DC voltage. The main disadvantage if this coupling method is that it causes some loss for the low frequency signals. However, for the low frequencies greater than 10 Hz, this coupling is the best and least expensive method. It is usually applied in small signal amplifiers, such as in record players, tape recorders, radio receivers, etc.

The R-C coupled two stage amplifier is multistage amplifier is shown in figure. In this amplifier two transistor \(Q_1\) and \(Q_2\) are connected in C-E emitter mode as in figure. The input signal is given to the base of first amplifier \(Q_1\) through coupling capacitor \(C_1\). The capacitor \(C_2\) couples the output of first amplifier across \(R_2\) with input of second amplifier through \(R_3\) . Thus it is called as R-C couple amplifier (resistance – capacitance) . The output \(Q_2\)that appears across \(R_4\) is coupled by \(C_3\) to the load resistor \(R_L\).

Circuit operation:

The circuit operation of R-C couple amplifier is as below:

1. The input signal \(v_{in}\) is amplified by amplifier \(Q_1\) which is in output of phase to that of input signal.
2. The coupling capacitor \(C_2\) couples the output of \(Q_1\) that appears across \(R_2\) to the \(R_3\) i.e. \(R_2-C-R_3\) forms the coupling network.
3. This coupled acts as input signal for amplifier \(Q_2\) which is in out of phase to that of input .
4. The amplified output of \(Q_2\) appear across \(R_4\) which is again reverse in phase.
5. The output of \(Q_2\) is coupled by \(C_3\) and appears across load resistor \(R_L\) which is twice reverse in phase.

Hence the output of RC- coupled amplifier in same phase to that of input signal . So that of there is no reversal phase in RC-coupled amplifier.

AC equivalent circuit:

The ac equivalent circuit of two stage amplifier (without showing source ) is shown figures .

Where,

$$ r_{i,1}=R_1 \parallel \beta_1 r_{e.1}’$$

$$ \simeq \beta_1 r_{e,1}’ $$

as \(R_1 >> \beta_1 r_{e.1}’\) is impedance of first stage amplifier and \(r_{o.1}=R_2 \parallel r_{i,2}\) is the output impedance of first stage. This because the \(r_{i,2}\) forms a component of output impedance of first stage.

The gain of first stage amplifier, i.e.

$$ A_{v1}=\beta_1 \biggl(\frac {r_{o,1}}{r_{i,1}} \biggr)$$

$$= \beta_1\biggl(\frac{r_{o,1}}{\beta_1 r_{e,1}’}\biggr)$$

$$=\frac{r_{o,1}}{r_{e,1}’}$$

$$A_{v1}=\frac {R_2 \parallel r_{i,2}}{r_{e1}’} \dotsm (1)$$

Thus the input impedance of second stage,i.e.

$$ r_{i,2}=R_3 \parallel \beta_2 r_{e,2}’$$

$$=\beta_2 r_{e,2}’$$ as \(R_3\) >>\( \beta_2 r_{e,2}’\)

And the output impedance of second stage,i.e.

$$ r_{o,2}=R_4 \parallel R_L$$ Where,$$r_{e,1}’=\frac {25mv}{I_{E.1}}$$ and $$r_{e,2}’=\frac{25mv}{I_{E.2}} $$ are the ac resistance across junction of first and second stage.

The gain of second stage,i.e.

$$ A_{v2}=\beta_2 \biggl(\frac{r_{o,2}}{r_{i,2}}\biggr)$$

$$=\beta_2 \frac {r_{o,2}}{\beta_2 r_{e,2}’}$$

$$=\frac{r_{o,2}}{r_{e,2}’} $$

$$A_{v2}=\frac{R_4 \parallel R_L}{r_{e,1}’} \dotsm(2)$$Hence the overall voltage gain RC coupled amplifier i.e.

$$A_v=\frac{V_{out}}{V_{in}} A_{v1} \times A_{v2}$$

$$=\frac{r_{o,1}}{r_{e,1}’} \times \frac{r_{o,2}}{r_{e,2}’}$$

$$A_V=\frac{(R_2\parallel r_{i,2})(R_4 \parallel R_L)}{r_{e.1}’ r_{e,2}’}$$

Cascade amplifier :

A cascade amplifier is any two- port network constructed form a series of amplifiers, where each amplifier sends its output to the input of the next amplifier in a daisy chain.

The complication in calculating the gain of cascade stages is the non-ideal coupling between stages due to loading, Two cascade common emitter stages are shown below. Because the input resistance of the second stage forms a voltage divider with the output resistance of the first stage, the total gain is not the product of the individual (separated) stages.

References:

(1)Theraja, B.L. Basic Electronics. N.p.: S.Chand, n.d. Print.

(2)C.L.Arora. Refresher Course in Physics. Vol. II and III. N.p.: S.Chand, 2006. Print.

(3)Malvino. Electronic Principles. N.p.: Tata McGraw-Hill, n.d. Print.

(4)N.Nelkon and P.Parker. Advanced Level Physics. 5th ed. N.p.: Arnold Heinemann, n.d. Print.

(5)Priti Bhakta Adhikari,Diya Nidhi Chaatkuli, Ishowr Prasad Koirala. A Textbook of Physics (2nd Year). N.p.: Sukunda Pustak Bhawan, 2070. Print