# JFET Source follower input impedance [duplicate]

I want to derive the input impedance of this JFET circuit :

simulate this circuit – Schematic created using CircuitLab

What is the method in order to derive the input impedance of this circuit?

here is the small signal but I haven't been able to deduce the equation of the input impedance

simulate this circuit

Zi=Vin/i

i=(Vgs+gm*Vgs*R3)/R1

Vin=Vgs*(1+gm*R3+gm*R4)+i*R4 = Vgs*(1+gm*R3+gm*R4)+(Vgs+gm*Vgs*R3)/R1*R4

Zi=((1+gm*R3+gm*R4)+(1+gm*R3)/R1*R4)/((1+gm*R3)/R1)

There is something wrong with these equations but I can't see my mistake...

• Here you will find the answer electronics.stackexchange.com/questions/372071/…
– G36
Sep 23, 2023 at 15:32
• You have to draw the equivalent circuit for incremental signals at the center of the band . Once this is done, analyze the circuit and find the input impedance by applying a test voltage source to the input. Sep 23, 2023 at 15:33
• "derivate" is a result of a calculation. I believe you want to "derive" the input impedance. Have you thought about using a simulation tool? Sep 23, 2023 at 15:40
• We see that R1 resistor current determines the Rin. Rin = Vin/I_R1 So we need to find the I1 resistor current. JFET gate current is 0A. So I_R1 current is: $$I_1 = \frac{V_{IN} - V_{OUT}\frac{R_4}{R_3 + R_4}}{R_1}$$ Additionally, we know that $V_{OUT} = A_V * V_{IN}$ So if we combine all the information we get Zin is equal to $$Z_{IN} = \frac{R_1}{1 - A_V \times \frac{R_4}{R_3 + R_4}}$$
– G36
Sep 24, 2023 at 7:53
• I see that you did manage to find the Zin. Your equation is correct. Good job.
– G36
Sep 24, 2023 at 12:44