AC Analysis common emitter configuration

[studentLab]

Hello and great day for all. Im asking for advice in this circuit. How to calculated Av for ac analysis in correct way.

Av1 =( R3//R6//R7// Beta(re +R9) ) / re+R9

Av2 = R8//R9 / re +R9

Using that formula i cannot get same with multisim simulator for Av1 and Av2

 

[LvW]

I see two small errors:
* First expression: Denominator (re+R4)
* Second expression: Numerator R8||R11 (instead of R8||R9).

 

[duke37]

I am not familiar with your // convention. All computer programs that I have used from algol onwards have just used brackets.

To look at Q2 in a simplified way, the voltage gain is the collector resistor/ emitter resistor.
The collector resistor is shunted by the load resistor, R11 so gain is 1.03k/1k = 1.03

Similarly, Q1 has a collector load of 1.2k so the gain is 8.

These calculations assume that the transistors have infinite gain and that the capacitors have zero reactance.

 

[(*steve*)]

R1 // R2 probably means 1/(1/R1 + 1/R2), i.e. R1 in parallel with R2

 

[LvW]

R1 // R2 probably means 1/(1/R1 + 1/R2), i.e. R1 in parallel with R2

Comparing in post#1 the circuit diagram with the formulas I think that the meaning of "//" is clear: parallel connection.

 

[studentLab]

Comparing in post#1 the circuit diagram with the formulas I think that the meaning of "//" is clear: parallel connection.

YEs im sorry my bad, it parallel. I fix the equation following LvW, and i get nearly same with simulator.

* ICq1 = IEq1
IEq1 = Vb1 - Vbe1 / R4 + R5
= 2.16 - 0.7 / 1k + 0.150k
= 1.27mA

* r'e get from r'e = Vt / ICq1 = 26mV / 1.27mA = 20.47 ohm.

Av1 =( R3||R6||/R7|| Beta(r'e +R4) ) / r'e+R4

Av1 = (3.6k x 10 / 3.6 + 10) || R7 || Beta(r'e +R4) ) / r'e+R4
Av1 = (2.647k x 2.2k / 2.647 + 2.2k) || Beta(r'e +R4) ) / r'e+R4
Av1 = (1.2k x (100x(20.47ohm + 150ohm)) / (1.2k + (100x(0.02047k + 0.150k)) / r'e+R4
Av1 = (1.2k x 17.04k) / (1.2k + 17.04k) / 0.02047k+0.150k
Av1 = 1.12k / 0.17k
Av1 = 6.59


Av2 = R8||R11 / r'e +R9
Av2 = ((3.6k x 1.5k) / (3.6k + 1.5k)) / 0.02047k + 1k
Av2 = 1.06k / 1.02k
Av2 = 1.04

 

[studentLab]

I am not familiar with your // convention. All computer programs that I have used from algol onwards have just used brackets.

To look at Q2 in a simplified way, the voltage gain is the collector resistor/ emitter resistor.
The collector resistor is shunted by the load resistor, R11 so gain is 1.03k/1k = 1.03

Similarly, Q1 has a collector load of 1.2k so the gain is 8.

These calculations assume that the transistors have infinite gain and that the capacitors have zero reactance.

Thank you duke37, it help me understand how to find voltage gain. But why simulator give 6.++ instead 8 for Av1?

 

[(*steve*)]

The simulator probably assumed something other than infinite gain in the transistor.

Assuming infinite gain for the transistor only works when the calculated stage gain is small compared with the actual transistor's gain.

The same thing is true for op-amps (that you may or may not have covered). However their open circuit gain is far higher than a single transistor and thus higher stage gains can be accurately predicted using the simple model that assumes infinite gain.

 

[studentLab]

Im confuse there diffrent formula to get Av:
Av = Vc / Vb
Av = Vout / Vin
Av = Rc / Re

In my DC analysis calculation:
VB1 = 2.16v
VC1 = 7.43v
VE1 = 1.46v

If i use
Av1 = VC1/VB1
= 7.43v / 2.16v
= 3.44

Av2 = Av1 since VB1, VC1 = VB2, VC2.

Av2 = 3.44

So in AC analysis i must use Av = RCtotal / REtotal right?

And when should i use Av = Vout / Vin?

 

[(*steve*)]

In the DC analysis, R_E is 1150 ohms.

In the AC analysis, R_E is 1000 ohms because the 150 ohm resistor is shunted by the much lower impedance of the capacitor (let's call it zero ohms)

 

[LvW]

Im confuse there diffrent formula to get Av:
Av = Vc / Vb
Av = Vout / Vin
Av = Rc / Re

In my DC analysis calculation:
VB1 = 2.16v
VC1 = 7.43v
VE1 = 1.46v
........

@studentLab:

1.) The gain of a circuit is a small-signal value (dynamic, differential) - hence, you must NOT use the ratio of DC values.
2.) The expression Av=Rc/Re is a rough estimate only. The correct formula is Av=Rc/(re+Re) with re=1/gm=Vt/Ic,
As you can see the rough approximation is valid for re<<Re only.
3.) The expression Vout/Vin is just the definition for gain and must be transferred to another formula (like the one in 2.) which contains parts values of the reöevant circuit.

 

[studentLab]

Thank you steve and LvW, it help me to understand better in this Av calculation. Only 2 month start studying Analog Measurement subject.

 

[duke37]

Gain of Q1
The simplified calculation assumes infinite transistor gain and neglected re. You calculated re as 20R so the emitter resistance is nearer 20 + 150 = 170
Gain calculation = 1200/170 = 7.0 which is very near the simulation of 6.9.

To get even closer, you could look at the effect of the reactance of the capacitors.

A good simulation saves a lot of work but even that is an approximation.