# Simulated voltage gain in Multisim differs very much from calculated

#### georgefrenk

Joined Dec 24, 2023
54
I am using Multisim software and I am comparing my calculated voltage gain with the one, done by Multisim.

Why is calculated Av ( -478.8 mV) much different from the one in simulation ( -990 mV) ?
I see the calculated is approx. half size of simulated.

I tried using virtual transistor instead of 2N2222A, but Ic and voltage gain stays almost the same.
And tried also moving PR2 voltage probe directly on 4 V power source.

Ic is seen as measured on schematic
Rc is seen on schematic
Vt is default 25 mV at room temparature
gm represents transconductance

gm = Ic / Vt = Ic / 25 mV
gm = 1.71 mA / 25 mV
gm = (0.0684 / 1000) S (Siemens)
gm = 0.0000684 S (Siemens)

Av = Rc * -gm
Av = 7000 ohm * -0.0000684 S
Av = -0.4788 V (volts)
Av = -478.8 mV

#### ericgibbs

Joined Jan 29, 2010
18,854
Hi george,
Welcome to AAC.
Why have you saturated the transistor in that circuit?
E

#### georgefrenk

Joined Dec 24, 2023
54
Hi george,
Welcome to AAC.
Why have you saturated the transistor in that circuit?
E
Even if I change source voltage from 4 V to 1 V, it doesn't change Ic and voltage gain.

#### Papabravo

Joined Feb 24, 2006
21,225
Even if I change source voltage from 4 V to 1 V, it doesn't change Ic and voltage gain.
The transistor is not biased in such a way that it can provide anything EXCEPT non-linear behavior. The DC bias should be approx Vcc/2 and you need an emitter resistor. Do you need a proper example of how a CE stage is built?

#### ericgibbs

Joined Jan 29, 2010
18,854
Hi g,
What voltages have you tried.
Don't forget you are not showing any Base bias voltages.
E

#### Papabravo

Joined Feb 24, 2006
21,225
Hi g,
What voltages have you tried.
Don't forget you are not showing any Base bias voltages.
E
Like this:

Notice the difference?
For the AC gain, it all comes down to your assumption of the internal emitter resistance.

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#### WBahn

Joined Mar 31, 2012
30,063
You seem to be confusing the DC voltage with the small-signal gain.

You are also being sloppy with your units. Av is a voltage gain -- it has units of V/V (or, in other words, it unitless). While you are at least carrying units through your work, you aren't actually tracking them. The product of ohms and siemens is 1.

The "DC gain" that Multisim is displaying is the ratio of the collector voltage (1.01 V) to the base voltage (1.02 V), which is pretty meaningless.

Your calculated Av is the gain for a small (AC) signal that is superimposed on the large (DC) signal. The whole small-signal analysis approach relies on the transistor being biased into the active region. But you are driving this poor transistor into deep saturation. Your base current is

Ib = (4 V - 1.02 V) / 50 Ω = 59.6 mA

This is nearly 35 times the collector current!

#### ericgibbs

Joined Jan 29, 2010
18,854
Hi george,
As this appears to be Homework, we can only give you guidance, not a final answer.

Do you know how to calculate the required Base bias resistors? To give, say a Collector voltage of Vsupply/2 ?

E

#### georgefrenk

Joined Dec 24, 2023
54
In the PDF, the beta of 200 is choosen, internal resistence of generator is 30 ohms. Frequency of generator is 10 kHz and voltage is 20 mV. I got adequate DC operating point as in PDF ( Ic = 4 mA, Ib = 0.02 mA). For PR2 output voltage probe, I uncheck "Negative reference probe". In Multisim, measured V(gain_AC) is 1.73, but my calculation is 0.1708. I got this by ((4.27 mA / 25 mV)/1000) * 1000 ohm.

#### georgefrenk

Joined Dec 24, 2023
54
Here I am including Multisim project file.

And I also checked input and output voltage with virtual oscilloscope and V(gain_AC) inside simulation appears to be correct.
It seems my equation(s) are not functioning.

#### Attachments

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#### georgefrenk

Joined Dec 24, 2023
54
Like this:
View attachment 310801
View attachment 310802
Notice the difference?
For the AC gain, it all comes down to your assumption of the internal emitter resistance.
I reconstructed this circuit, for which you posted image in your reply. And I measured V(gain_AC), which appears as 113.
And V(gain_DC) appears as changing through time.
Is this value 113 correct value for AC gain? Must AC gain be measured in different way inside Multisim?

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#### georgefrenk

Joined Dec 24, 2023
54
Like this:
View attachment 310801
View attachment 310802
Notice the difference?
For the AC gain, it all comes down to your assumption of the internal emitter resistance.
is "av: vorms/virms=102.346" on your photo actually gain for AC voltage
and on right side, "Av = ..." is gain for DC?

#### Jony130

Joined Feb 17, 2009
5,488
is "av: vorms/virms=102.346" on your photo actually gain for AC voltage
Yes, this is the AC gain measured in LTspice Vout/Vb. And this gain does not include the Rsig effect on the total gain.

and on right side, "Av = ..." is gain for DC?
No, DC gain has no meaning in this type of a amplifier because this is not a DC amplifier, thus we have only AC gain.
Av is an AC gain that we computed from this equation Av ≈ RL/re.
For Ic =1mA --- > re = 26mV/1mA = 26Ω therefore Av ≈ 3kΩ/26Ω = 115 V/V

#### georgefrenk

Joined Dec 24, 2023
54
For upper circuit with ZTX1048A, I calculated AC gain with:
// Ic = 1.01 mA is taken as measured in Multisim
gs (conductance) = Ic / 25 mV = (1.01 mA / 25 mV) / 1000 = 0.0000404;
Vac = -gs * Rc = -0.0000404 * 3010 = -0.121;

Why such a difference between measured (113) and calculated (-0.121) voltage AC gain?
I suppose value 113 is correct one. Is there a reason why not use above two equations?

#### Jony130

Joined Feb 17, 2009
5,488
. In Multisim, measured V(gain_AC) is 1.73, but my calculation is 0.1708. I got this by ((4.27 mA / 25 mV)/1000) * 1000 ohm.

Av ≈ (Rc||Rc4)/(re + Rc6) ≈ (1kΩ||50Ω)/(6Ω + 20Ω) = 1.8 [V/V]
gs (conductance) = Ic / 25 mV = (1.01 mA / 25 mV) / 1000 = 0.0000404;
Vac = -gs * Rc = -0.0000404 * 3010 = -0.121;

Why such a difference between measured (113) and calculated (-0.121) voltage AC gain?
I suppose value 113 is correct one. Is there a reason why not use above two equations?
Why do you divide gm (gs) by 1000? For what reason?

#### georgefrenk

Joined Dec 24, 2023
54
Ok, I see. Both Ic and 25 mV are in milis, so no need to divide by 1000.
Now the calculated value is 121.6 , which is much closer to 113.
Thank you.

#### Papabravo

Joined Feb 24, 2006
21,225
is "av: vorms/virms=102.346" on your photo actually gain for AC voltage
and on right side, "Av = ..." is gain for DC?
The estimate of re', in units of ohms, for a given transistor can vary from a low of 26 mV/mA to 52 mV/ma. It is a function of temperature. So the value that you choose depends on temperature. In my case I chose a value just below the mean value to represent operating at the temperature of 37 °C. Since the β of a transistor cannot be tightly controlled or specified, I chose to ignore the actual β of the transistor that I simulated and went with the specification of the problem in the text.

The calculated gain, ignoring the minus sign, was 81.1 based on the assumption that re' was 37Ω. In the simulation it came out to 102.346 which would be the case if and only if the β of the transistor was 150 and the value of re' was 29.3Ω. The discrepany would be a clue that one of our assumptions of reality did not hold in the simulation which would lead us to ask two followup questions:
1. What is the actual value of β for the transistor
2. What is the actual value of re' given a specific temperature.
Point #2 would only be valid if the model takes temperature into account.

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