Small Signal - Low frequency - Analysis of Common Base amplifier.. Yes, the characteristics of a CB amplifier is analyzing using low frequency -small amplitude signal. Analysis of CE amplifier is in another post. Better to go through it before diving into this.
As discussed in previous posts, analysis requires three steps - 1)Taking the circuit which is to be analyzed 2)obtaining the small signal model and 3)finding out equations for parameters helps to get approximate values and it in turn will help to predict the characteristics of the circuit.
The figure below shows a Common base amplifier. A signal ground is attached to the base terminal. Emitter is turn into input terminal by attaching an input source Vs through Rs and C1. Output is taken across RL, connected to the collector of the transistor. DC voltage Vcc provides biasing at the output terminal and a constant current biasing is provided at the input terminal.
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| fig 1 |
So the first part is over, we got the circuit. Second part is to draw the equivalent circuit. As in earlier post we can take a hybrid π model. But here it is recommended to use 'T-model'.
2. Obtain small signal equivalent model (Please see 'Small signal model of a circuit' )
Steps 1: D C voltage sources are replaced by ground
2: D C current sources are open circuited
3: Capacitors are shorted
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| fig 2 |
4,5: Rearrange the components to have a common ground and insert transistor model
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| fig 3 |
For analyzing behavior of a transistor we depends mainly on four parameters:
a): Input resistance (Rin)
Input resistance of the circuit can be calculated by 'looking into the
input side of the circuit' from the mark as given in fig 3. This is
because RS is taken as a source resistance and usually not consider for input resistance calculation.
From the above circuit, Rin = re ---------(1)
CB amplifier has a low input resistance because the value of re is usually a few ohms to few tens of ohms.
b): Output resistance (Ro )
Again to get the output resistance, look into the circuit from right side of arrow.
Then from the circuit, Ro = Rc ----------(2)
c): Voltage gain (Av)
Voltage gain (Av) is defined as
Av = Vo / Vi where,
Vo = output voltage and
Vi = input voltage appear across the input terminal(here Base) of the amplifier.
Vi = -ie re -----------(3)
Output voltage(Vo) is the voltage across the parallel combination of Rc and RL. Vo = -αie(Rc ‖ RL) ------------(4)
Now we can write an expression for Av.
Av = Vo / Vi
-----------(5) For T-model, α/re = gm . Using this equ(5) can be written as
Av = gm (Rc ‖ RL) ------------(6)
Here, Av has a positive sign.It means the output and input waveforms have the same polarity. So CB is a non inverting amplifier.
Another parameter related to voltage gain is overall voltage gain. The overall voltage gain for the circuit in fig 3 is given as Gv
= Vo / Vs . We can easily get it as
Here Vo/Vi is in our hand. Now find an equ for Vi/Vs
--------------(7)Overall voltage gain is Gv is obtained by multiplying equ (5) and (6).
--------------(8)d): Current gain (A is)
Here short circuit current gain is considered. That is the current gain when RL is shorted. From fig 9, when RL is shorted, output current is
ios = - α ie .
The input current is marked in fig 3 as ii = - ie .
Short circuit current gain (A is) = ios / ii .
A is = α ------(9)
Current Buffer
Since α ≈ 1, we can conclude that, short circuit current gain of CB amplifier is nearly unity. Because of this property it can act as a current buffer. It means current at the output terminal is same as that at the input terminal.
This analysis is given in the text book: Micro Electronics by Sedra & Smith. It is presented here with detailed description.
This analysis is given in the text book: Micro Electronics by Sedra & Smith. It is presented here with detailed description.