Transistor Problem: Finding Voltage Gain in Common Emitter Circuit

[lazyaditya]

The circuit is shown below and i am asked to find out the voltage gain A(v)

Beta = 100 and Vcc = 13.7 volts Common emitter configuration.

Voltage Gain is equal to the ratio of output voltage to input voltage .

The Attempt at a Solution

Don't know how to proceed as there wasn't any v(i) or v(o) given in the equation, how should i start ?

 

[Ratch]

lazyaditya,

Don't know how to proceed as there wasn't any v(i) or v(o) given in the equation, how should i start ?

If you input 1 volt, what would the change in output voltage be?

Ratch

 

[lazyaditya]

if i would know what will be the currents across 100 kohms, 12 kohms and 10 kohms i can use kvl including v(i), but then i wouldn't know what v(cb) is ? Voltage gain is ratio of output to input right then how am i supposed to know output voltage since beta is multiplied with input current giving i(c) value which will passed through load resistant to give output voltage ! i think that's how single stage amplifier works ?

 

[Ratch]

Lazy,

Why are you worrying about the current through the 100k resistor? Most all your signal current will exist the the base-emitter path. If you know the current change in the base circuit, then you know the current change in the collector, right? And when you know the current change in the collector, then you know the voltage change across the 12k resistor.

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[lazyaditya]

ya but how should i find that base current ? and without considering 100 kohms i have to consider v(ce) for kvl ! isn't that so ?
or else how would i be able to calculate i(b) ?

 

[Ratch]

Lazy,

I told you already. The 100k value is so much higher than the base-emitter resistance that almost no signal will flow through it. So it can be ignored for small signal analysis.

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[lazyaditya]

i got the solution right now and the person is considering 100 kohm as the part for conduction i am posting the solution over here please help , i am not able to understand !

 

[lazyaditya]

here it is !

 

[Ratch]

Lazy,

Base current change in the base-emitter junction for 1 volt input will be 1/10k = 0.1ma. Multiply base current by beta gives 10ma collector current change. Multiply collector current by 12k gives 120volts. So small signal gain is 120/1 = 120

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[lazyaditya]

but A(v) is 10

 

[Ratch]

Lazy,

So where did I go wrong? Find my mistake.

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[lazyaditya]

do we calculate the voltage across Rc or across load resistance that will be emitter resistance i guess ? And isn't the 13.7 volts the biasing voltage ! won't it affect the base current in some manner ?

 

[lazyaditya]

plus we are just assuming it to be having 1 volt input signal and considering it small signal analysis giving linear model ! can't it be large signal in which each gap in Ib will create non linear effects in Ic!

 

[lazyaditya]

according to the solution given to me i wasn't able to understand the equivalent circuit the person has drawn !

 

[Ratch]

Lazy,

What is there about my analysis you don't understand?

Ratch

 

[lazyaditya]

ya i understood it !