MOSFET Small Signal Model

MOSFET Small Signal Model

• From Fig. 7.1.1, we see that the output voltage is

V_DS = V_o = V_DD - i_D R_D

• Using equation (7.2.6) of section 7.2 , we obtain

V_o = V_DD - (I_DQ + i_d)R_D

= (V_DD - I_DQ R_D) - i_d R_D

• The output voltage is also a combination of d.c. and a.c. values. The time-varying output signal is the time-varying drain-to-source voltage, or

V_o = V_ds = - i_dR_D   ...(7.3.3)

• Also, from equations (7.2.6) and (7.2.7) of section 7.2, we have

i_d = g_m V_gs

• In summary, the following relationships exist between the time-varying signals for the circuit in Fig. 7.1.1 (a). The equations are given in terms of the instantaneous a.c. values, as well as the phasors. We have,

• The Fig. 7.3.1 shows the a.c. equivalent circuit. Here, the d.c. sources in Fig. 7.1.1 are made zero.

• From the equivalent circuit for the NMOS amplifier circuit, we can draw a small signal equivalent circuit for the MOSFET.

• The Fig. 7.3.2 (b) shows the small signal low frequency a.c. equivalent circuit for n-channel MOSFET.

• The relation of Id by Vgs is included as a current source gmv gs connected from drain to source. 

• The input impedance is represented by the open circuit at its input terminals, since gate current I_G is zero.

• We know that the circuit has the finite output resistance of a MOSFET biased in the saturation region because of the nonzero slope in the ip versus VDS curve. We also know that,

i_D = K[(v_GS-V_T)²(1+ λv_DS)] ... (7.3.8)

where λ  is the channel-length modulation parameter and is a positive quantity. The small signal output resistance, is defined as,

• This small signal output resistance is also a function of the Q-point parameters. The Fig. 7.3.3 shows the small signal equivalent circuit of common-source circuit shown in Fig. 7.1.1.

Ex. 7.3.1 For the circuit shown in Fig. 7.3.4. MOSFET parameters are: V_T = 1 V, K = 0.80 mA/V², and λ = 0.01 V_T -1. Determine the small signal voltage gain of a MOSFET circuit. Assume the transistor is biased in the saturation region.

Sol. :

Step 1: Calculate I_DQ g_m and r_o

 The quiescent values are,

Step 2: Draw the small signal ac equivalent circuit.

Step 3: Calculate voltage gain

Look at Fig. 7.3.5, we have

V_o  = -g_m V_gs (r_o ||R_D)

Since v_gs  = V_i,

The small signal voltage gain is,

Ex. 7.3.2 For the circuit shown in Fig. 7.3.6, if V_TN = 1 V, K_n = 0.8mA/V₂, λ = 0.01 V^-1, determine small signal voltage gain. Assume that EMOSFET is biased in saturation and V_GSQ = 3V

Sol. :

Step 1 : Calculate I_DQ , g_m and I_o

Ex. 7.3.3 Determine the small signal voltage gain of a MOSFET circuit shown in Fig. 7.3.7. Assume VGSQ = 2.12 V, VDD = 5 V, RD = 2.5 kQ. Assume transistor parameters are VT = 1 V, K = 0.80 mA/V7 and λ = 0.02/V. Assume the transistor biased in the saturation region.

Sol .:

The quiescent Values are,

Important Concept

• Because of the relatively low value of transconductance, MOSFET circuits tend to have a lower small signal voltage gain than comparable bipolar circuits.

• The negative sign in the gain indicates that the sinusoidal output voltage is 180 degrees out of phase with respect to the input sinusoidal signal. 

1. Steps in the A.C. Analysis of MOSFET Amplifier

• The steps to be performed in the analysis of the MOSFET amplifier are as follows:

1. Perform the d.c. analysis of the circuit and check whether the MOSFET is biased in the saturation region in order to produce a linear amplifier.

2. Replace the MOSFET by its small signal equivalent circuit.

3. Analyze the small signal equivalent circuit, making the d.c. source components equal to zero.

2. CS MOSFET Amplifier with p-channel MOSFET

• The Fig. 7.3.8 shows the common source circuit with p-channel MOSFET and its a.c. equivalent circuit.

• The a.c. equivalent circuit seen for n-channel MOSFET also applies to the p-channel MOSFET; however, there is a change in current directions and voltage polarities compared to the circuit containing the n-channel MOSFET.

• The Fig. 7.3.9 shows the small signal equivalent circuit of the p-channel MOSFET amplifier.

Important Concept

• It is important to note that the expression for the small signal voltage gain of the p-channel MOSFET amplifier is exactly the same as that for the n-channel MOSFET amplifier.

• The negative sign indicates that a 180- phase reversal exists between the output and input signals, for both the PMOS and the NMOS circuits.

Review Questions

1. Draw and explain the small signal equivalent circuit of MOSFET.

2. Describe about small signal MOSFET amplifiers (NMOS) and obtain the expression for it's transconductance.