# Computing Input Impedance, Output Impedance And Voltage Gain

#### aac044210

Joined Nov 19, 2019
178
Hi:

I have attempted to compute input impedance, output impedance, and voltage gain
for each stage and overall voltage gain for an audio amplifier circuit (schematic attached).

I did not attempt the output impedances because I am lost there.

The sim gives an overall voltage gain of 588, so I know that I have made at least one
error. Schematic added by a moderator. Note: The missing component on the base of
Q3 is a pot.

My attempt:
 r'e4 = 25.86 mV / IE4 1.019​ Ω re4 = RE31║RL 0.001​ KΩ Zin4(Base) = βac4 * (re'4 + re4) 0.202​ KΩ Zin4 = Zin4(Base) 0.202​ KΩ Zout4 ? Av4 = re4 / r'e4 0.981​ r'e2 = 25.86 mV / IE2 1.800​ Ω rc2 = RB3║Zin4 0.168​ KΩ Zin2(Base) = βac2 * (r'e2 + RE2) 11.112​ KΩ Zin2 = RB2║Zin2(Base) 0.845​ KΩ Zout2 ? Av2 = rc2 / (r'e2 + RE2) 1.650​ r'e1 = 25.86 mV / IE1 2.660​ Ω rc1 = RC1║Zin2 0.458​ KΩ Zin1(Base) = βac1 * (r'e1 + RE1) 100.266​ KΩ Zin1 = RB1║Zin1(Base) 3.466​ KΩ Zout1 ? Av1 = rc1 / r'e1 172.180​ Av(Total) = Av1 * Av2 * Av4 278.749​ Overall Voltage Gain Per Sim 588.000​
aac

#### Attachments

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#### BobaMosfet

Joined Jul 1, 2009
1,979
Can you post the schematic in another format.... jpg, gif, tif, pdf?

#### aac044210

Joined Nov 19, 2019
178
Hi:

I have attempted to compute input impedance, output impedance, and voltage gain
for each stage and overall voltage gain for an audio amplifier circuit (schematic attached).

I did not attempt the output impedances because I am lost there.

The sim gives an overall voltage gain of 588, so I know that I have made at least one
error.

View attachment 198915
Schematic added by a moderator. Note: The missing component on the base of
Q3 is a pot.

My attempt:
 r'e4 = 25.86 mV / IE4 1.019​ Ω re4 = RE31║RL 0.001​ KΩ Zin4(Base) = βac4 * (re'4 + re4) 0.202​ KΩ Zin4 = Zin4(Base) 0.202​ KΩ Zout4 ? Av4 = re4 / r'e4 0.981​ r'e2 = 25.86 mV / IE2 1.800​ Ω rc2 = RB3║Zin4 0.168​ KΩ Zin2(Base) = βac2 * (r'e2 + RE2) 11.112​ KΩ Zin2 = RB2║Zin2(Base) 0.845​ KΩ Zout2 ? Av2 = rc2 / (r'e2 + RE2) 1.650​ r'e1 = 25.86 mV / IE1 2.660​ Ω rc1 = RC1║Zin2 0.458​ KΩ Zin1(Base) = βac1 * (r'e1 + RE1) 100.266​ KΩ Zin1 = RB1║Zin1(Base) 3.466​ KΩ Zout1 ? Av1 = rc1 / r'e1 172.180​ Av(Total) = Av1 * Av2 * Av4 278.749​ Overall Voltage Gain Per Sim 588.000​
aac
You just don't have the pot model in your database. It is on the schematic.

#### aac044210

Joined Nov 19, 2019
178
Can you post the schematic in another format.... jpg, gif, tif, pdf?

#### Jony130

Joined Feb 17, 2009
5,333
Very strange because my simulation is showing AV_total ≈ 700 [V/V] (AC analysis).

overall voltage gain of 588
How did you determine the voltage gain?

re4 = RE31║RL

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#### aac044210

Joined Nov 19, 2019
178
Very strange because my simulation is showing AV_total ≈ 700 [V/V] (AC analysis).

How did you determine the voltage gain?

Av(Total = 5.466 volts / 9.3 mV = 588 per the sim.

#### Jony130

Joined Feb 17, 2009
5,333
And this 5.466 volts comes from what type of analysis?

#### aac044210

Joined Nov 19, 2019
178
And this 5.466 volts comes from what type of analysis?
The measurement comes from the "ac analysis" in the sim. I have attached the
sim file again just in case the file you have is corrupted.

#### Attachments

• 4.8 KB Views: 3

#### Jony130

Joined Feb 17, 2009
5,333
Well, it that case you must be using the different 2N3904JP model then I use, end of the story. But nevertheless, I already show you where did you make the error in your calculations (here re4 = RE31║RL ).

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• Zeeus

#### Audioguru again

Joined Oct 21, 2019
4,673
The amplifier will have horrible distortion without any negative feedback.

• Zeeus

#### MrAl

Joined Jun 17, 2014
8,978
Hello guys,

I was getting a much higher than expected gain doing a straight nodal analysis compared to what i was reading so far in this thread so i had to look into this.
What i found was very simply that the overall gain is HIGHLY dependent on the transistor models.
So i changed the 2N3904's to 2N3904a and set the model statement to 1e-14 and 100 as we had been using before, and looked up the params for the TIP transistors and set them to these values:
.model TIP31C NPN(BF=293 IS=599e-15)
.model TIP32C PNP(BF=527 IS=1.8E-12)
and of course the 2N3904a was set to:
,model 2N3904a NPN(BF=100 IS=1e-14)

But before i did that, i changed only one transistor and the gain went from 592 to over 700 so i was sure the model changes the gain significantly.
Anyway, with the above models i get around 1163 for the gain. See what i mean?

Oh yeah BTW i set the upper "pot" resistor to 725 and lower "pot" resistor to 745 because that is what the schematic says in the lower right hand corner. So there is no pot just two resistors now.

My suggestion is that if you both want to see the same gain figures then use the same model statements rather than depend on some undisclosed models. Note that the 2N3904 in my simulator has BF=300 not 100, and that is the same with the MicroCap variation, so there is a lot of variation in models. Using a model statement for each transistor will convey the model information for anyone and everyone reading this thread so anyone trying to repeat the results will get the same outcome.
If for some reason you are unhappy with those model statements simply post the ones you want to use and we can all get onto the same page with this.

Last edited:

#### aac044210

Joined Nov 19, 2019
178
Hello guys,

I was getting a much higher than expected gain doing a straight nodal analysis compared to what i was reading so far in this thread so i had to look into this.
What i found was very simply that the overall gain is HIGHLY dependent on the transistor models.
So i changed the 2N3904's to 2N3904a and set the model statement to 1e-14 and 100 as we had been using before, and looked up the params for the TIP transistors and set them to these values:
.model TIP31C NPN(BF=293 IS=599e-15)
.model TIP32C PNP(BF=527 IS=1.8E-12)
and of course the 2N3904a was set to:
,model 2N3904a NPN(BF=100 IS=1e-14)

But before i did that, i changed only one transistor and the gain went from 592 to over 700 so i was sure the model changes the gain significantly.
Anyway, with the above models i get around 1163 for the gain. See what i mean?

Oh yeah BTW i set the upper "pot" resistor to 725 and lower "pot" resistor to 745 because that is what the schematic says in the lower right hand corner. So there is no pot just two resistors now.

My suggestion is that if you both want to see the same gain figures then use the same model statements rather than depend on some undisclosed models. Note that the 2N3904 in my simulator has BF=300 not 100, and that is the same with the MicroCap variation, so there is a lot of variation in models. Using a model statement for each transistor will convey the model information for anyone and everyone reading this thread so anyone trying to repeat the results will get the same outcome.
If for some reason you are unhappy with those model statements simply post the ones you want to use and we can all get onto the same page with this.
Hi:

Thanks MrAl. I have modified my sim to agree to yours and I also have a gain of 1162. I will re-do my hand calculations
and see what I can come up with and then re-post them.

aac

Last edited:

#### MrAl

Joined Jun 17, 2014
8,978
Hi:

Thanks MrAl. I have modified my sim to agree to yours and I also have a gain of 1162. I will re-do my hand calculations
and see what I can come up with and then re-post then.

aac
Ok sounds good.

#### Jony130

Joined Feb 17, 2009
5,333
Stage 1 voltage gain looks too optimistic compared to the sim results.

Av1 = (12k||10.1k||1k||0.993k)/2.66Ω = 456Ω/2.66Ω = 171 V/V

Also in AC analysis, you are kept using this statement .ac dec 111 1 1000k And because of this, you don't see the capacitor effect on the voltage gain (effect on amplifier bandwidth).

In this case, the capacitor will have an effect on a voltage gain value at 1kHz. Also why you keep using AC = 8mV instead of a 1V and get a voltage gain value directly from LTspice without the need of using any additional calculation is beyond me. The output stage output voltage is a voltage across RL resistance, and this is not the same as R31+RL.

#### aac044210

Joined Nov 19, 2019
178
Stage 1 voltage gain looks too optimistic compared to the sim results.

Av1 = (12k||10.1k||1k||0.993k)/2.66Ω = 456Ω/2.66Ω = 171 V/V

Also in AC analysis, you are kept using this statement .ac dec 111 1 1000k And because of this, you don't see the capacitor effect on the voltage gain (effect on amplifier bandwidth).

In this case, the capacitor will have an effect on a voltage gain value at 1kHz. Also why you keep using AC = 8mV instead of a 1V and get a voltage gain value directly from LTspice without the need of using any additional calculation is beyond me.

View attachment 199013
The output stage output voltage is a voltage across RL resistance, and this is not the same as R31+RL.
I don't see this statement on my sim .ac dec 111 1 1000k .

Where is this coming from? Av1 = (12k||10.1k||1k||0.993k)/2.66Ω = 456Ω/2.66Ω = 171 V/V

#### Jony130

Joined Feb 17, 2009
5,333
I don't see this statement on my sim .ac dec 111 1 1000k .
Ups, this is mine, yours is here:
.ac dec 10 1000 1000

Where is this coming from? Av1 = (12k||10.1k||1k||0.993k)/2.66Ω = 456Ω/2.66Ω = 171 V/V
Av1 = (Rc1||Rb21||Rb22||Zin_2)/re2

Zin2 = (hfe +1)*(re2 + RE2)

Last edited:

#### aac044210

Joined Nov 19, 2019
178
Ups, this is mine, yours is here:
.ac dec 10 1000 1000

Av1 = (Rc1||Rb21||Rb22||Zin_2)/re2

Zin2 = (hfe +1)*(re2 + RE2)
thanks

#### aac044210

Joined Nov 19, 2019
178
Shouldn't Zin2 = RB21|| RB22 || (βac2 * (r'e2 + RE2) ?

and

Av1 = RC1||Zin2 / r'e1 ?

#### Jony130

Joined Feb 17, 2009
5,333
Shouldn't Zin2 = RB21|| RB22 || ((βac2 +1)* (r'e2 + RE2) ?

and

Av1 = RC1||Zin2 / r'e1 ?
Sure you can use it too. It is the same as mine "equation" if you add +1 to the beta vale.
So it doesn't matter which one you use in the end.

#### MrAl

Joined Jun 17, 2014
8,978
Stage 1 voltage gain looks too optimistic compared to the sim results.

Av1 = (12k||10.1k||1k||0.993k)/2.66Ω = 456Ω/2.66Ω = 171 V/V

Also in AC analysis, you are kept using this statement .ac dec 111 1 1000k And because of this, you don't see the capacitor effect on the voltage gain (effect on amplifier bandwidth).

In this case, the capacitor will have an effect on a voltage gain value at 1kHz. Also why you keep using AC = 8mV instead of a 1V and get a voltage gain value directly from LTspice without the need of using any additional calculation is beyond me.

View attachment 199013
The output stage output voltage is a voltage across RL resistance, and this is not the same as R31+RL.
Hi,

I ended up using 1mv so i could read the gain directly from the voltage without disturbing the bias point too much. So if the gain was 123 i would read 0.123v output which is easy to convert.

I also found that the gain of the first stage is highly dependent on the dynamic resistance of the BE diode. 0 Ohms leads to a gain of 991 while 3 Ohms leads to just 161, which is quite different. This in turn tells me the first stage should maybe be redesigned.