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# How to get Vgs equation for MOSFET Small Signal Equivalent Model ?

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#### narayani

Dear Friends,

In attachment, I have shown two Small Signal Equivalent Models of MOSFET for finding out Vgs.
In First Small Signal Equivalent Model of MOSFET, I have found out Vgs = Vg= (Vin R1//R2)/(Rg+R1//R2), because R1//R2 parallel with the Vin and Rg. Using Voltage divider, I found Vgs=Vg=(Vin R1//R2)/(Rg+R1//R2).

In Second Small Signal Equivalent Model of MOSFET shown in the attachment, I need to find out Vgs. In the Second Small Signal Equivalent Model of MOSFET shown in the attachment, I have removed the R1//R2 for my own circuit. What is the Vgs equation for the Second Small Signal Equivalent Model of MOSFET, when R1//R2 is not Parallel with the Vin and Rg (source generator resistance).

Can you help me to find out Vgs equation for Second Small Equivalent Circuit shown in the attachment, when R1// R2 are not present in the SSM of MOSFET.

#### Attachments

• Small_Signal_Model_of_MOSFET.pdf
204.5 KB · Views: 132

Well, since your Voltage Source is "seeing" an infinite impedance, I would say that your Vgs is equal do Vin. If you consider a resistance, Rp, between G and ground, if you apply the voltage divider equation you will get: Vg = (Vin*Rp)/(Rp + Rg); Since Rp >> Rg, you will have Vg ~= (Vin*Rp)/Rp, so, Vg is equal to your input voltage.

But wait for someone else opinion.

With best regards.

P.S. - In practise you observe exactly that. Image that you mount your MOSFET on a breadboard, and you connect your signal source to the gate of your mosfet. The signal applied at the gate of your mosfet will be all the voltage that you programme your signal generator to output, even though your signal generator has an internal 50 Ohm impedance.

narayani

### narayani

Points: 2
Well, since your Voltage Source is "seeing" an infinite impedance, I would say that your Vgs is equal do Vin. If you consider a resistance, Rp, between G and ground, if you apply the voltage divider equation you will get: Vg = (Vin*Rp)/(Rp + Rg); Since Rp >> Rg, you will have Vg ~= (Vin*Rp)/Rp, so, Vg is equal to your input voltage.

But wait for someone else opinion.

Dear Sir,
As you asked I am not considering Rp between G (gate) and Ground, Vin is in series with Rg as shown in the attachment of posting #1. What is the Equation for Vg.

Well, since your Voltage Source is "seeing" an infinite impedance, I would say that your Vgs is equal do Vin. If you consider a resistance, Rp, between G and ground, if you apply the voltage divider equation you will get: Vg = (Vin*Rp)/(Rp + Rg); Since Rp >> Rg, you will have Vg ~= (Vin*Rp)/Rp, so, Vg is equal to your input voltage.

But wait for someone else opinion.

Dear Sir,
As you asked I am not considering Rp between G (gate) and Ground, Vin is in series with Rg as shown in the attachment of posting #1. What is the Equation for Vg.

Exactly. Vg is equal to Vin. You can use that Rg to help you to understand what happens. For instance, if Rg as a zero Ohm value, you would have a shot circuit, but when Rg is infinite, you have a open circuit, just like you draw in your small signal equivalent model.. So, what I previously said was with the intention to help you.

With best regards.

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