High-Frequency Response of FET Amplifiers

High-frequency response of an FET amplifier is similar to that of a BJT amplifier. Figure below shows the high-frequency model for an FET (JFET as well as MOSFET). As we can see from the figure, the high-frequency model is similar to the low-frequency model with the addition of junction capacitances.

High-frequency model of a FET

The capacitance C_gs represents the barrier capacitance between the gate and the source terminals. C_gd is the barrier capacitance between the gate and the drain terminals. C_ds is the drain-to-source capacitance of the channel. These capacitors offer high impedance at lower frequencies and can be considered as open circuit. However, at high frequencies, due to these capacitances feedback exists between the input and output circuits and voltage amplification drops rapidly as the frequency increases.

Common-source JFET amplifier

Figure below shows the high-frequency equivalent model for the common-source JFET amplifier.

High-frequency model for the common-source JFET amplifier

Output voltage V_o is given by the product of short-circuit current (I) and the impedance seen among the output terminals (Z). Therefore,

Z is determined by shorting the input terminals, that is, V_s = 0. Hence, there is no current flowing through the current generator g_mVs. Therefore, the value of Z is given by the parallel combination of R_L, C_ds, rd and C_gd and is given by

Where, G_L = 1/R_L is the conductance corresponding to load R_L If the load is represented by an impedance Z_L, then G_L will be replaced by Y_L (Y_L is the admittance corresponding to impedance Z_L). Also Y_ds = j ω C_ds is the admittance corresponding to C_ds; g_d = 1/rd is the conductance corresponding to rd; Y_gd = j ωC_gd is the admittance corresponding to C_gd. The current I flowing from the drain to the source terminal with output terminals shorted is given by

Therefore, the output voltage V_o is given by

The value of voltage gain (A_v) is equal to

At low frequencies, the FET capacitances can be neglected and hence Y_ds = Y_gd = 0. Therefore, the value of gain at low frequencies is given by

Where

As we can see from the high-frequency model in Q2 that there is a coupling between the gate and the drain terminals through capacitance C_gd. The admittance offered by the capacitance (Y_gd) can be replaced by Ygd(1 – A_V) between the gate and the source terminals and by Y_gd[1 – (1/A_V)] between the drain and the source terminals. The input admittance (Y_i) is therefore given by

The input capacitance (C_i) is given by

Input capacitance is important in the case of cascaded amplifiers where the input impedance of a stage acts in shunt across the output impedance of the preceding stage. As the reactance of a capacitance decreases with frequency, the input impedance decreases and hence the gain of the cascaded amplifier also decreases with increase in frequency.

The output impedance is obtained by the impedance looking into the drain and the source terminals, with the input voltage (Vi) set equal to zero. With V_i = 0, the resistance rd and capacitances C_ds and C_gd are in parallel. Therefore, the output admittance (Y_o) is given by

Common-drain amplifier (source-follower amplifier)

Figure below shows the small-signal high-frequency equivalent circuit of the common-drain amplifier.

Output voltage V_o is given by the product of the short-circuit current and the impedance between the source and the ground terminals. Voltage gain can be obtained in a manner similar to that for the common-source amplifier. The expression for the voltage gain (A_v) for a common-drain amplifier is given by

At low frequencies, the value of reactance offered by the capacitances C_gs, C_ds and C_sn is infinity. Therefore, at low frequencies, the value of voltage gain (A_v) is given by

The value of Av is slightly less than unity as generally g_mR_s >> 1.

Input admittance (Y_i) is obtained by using the Miller’s theorem in a manner similar to that done for the common-source FET amplifier. The expression for (Y_i) is given by

One of the major advantages of the common-drain amplifier over the common-source amplifier is that it offers lower input capacitance as compared to the common-source amplifier.

The output admittance (Y_o) can also be determined in a manner similar to that for the common-drain FET amplifier. It is given by