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When considering channel length modulation, draw an equivalent circuit and use it to obtain the voltage gain. (Assume that it operates in the saturation mode)

When considering channel length modulation, draw an equivalent circuit and use it to obtain the voltage gain. (Assume that it operates in the saturation mode)

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When considering channel length modulation, draw an equivalent circuit and use it to obtain the voltage gain. (Assume that it operates in the saturation mode)

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Draw an equivalent circuit considering the channel length and use it to obtain the voltage gain (The current source is ideal. Assume that all Transistors operate in the saturation mode)
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Consider MOSFET-based current source circuits shown below. Assume that the n-type MOSFET transistors follow the long-channel model with μnCox = 100 μA/V2 and Vth,n = 0.5 V. All the transistors have a fixed channel length L = 0.25 μm. The bias voltage VB1 is at 0.8 V. Assume that all transistors have no back-bias effect. (1) (2) (a) For a basic current source in Fig. (1), size the NMOS transistor M1's width ( = W1) so that it conducts a current of 1 mA when it operates in saturation region. You may assume λn = 0. (b) What is the minimum value of Vout for this circuit that keeps M1 in saturation region? (c) For a cascode current source in Fig. (2), assume that the transistor M2 has the same width with M1 you determined from part (a). Determine the value of VB2 that yields the lowest minimum VOUT keeping both M1 and M2 in saturation regions. (d) Now, let's assume that the transistors M1 and M2 have a finite output resistance with λn = 0.1 V−1. Compute the value of the output resistance (Rout) of this cascode current source when M1 and M2 are in the saturation region. (Hint: Calculate the output impedance in a small signal equivalent circuit.)
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6. Fig. 6 shows a cascode current mirror. Assume that (W/L)M1 = (W/L)M2 = (W/L)M3 = n1•(W/L)M4, IREF = 20 µA.Vtn = 0.7 V for all transistors and |Vov| = 0.2 V for all transistors except M4. (a) To design IOUT = IREF without considering channel-length modulation, please calculate n1 to minimize the allowable output voltage Vout while all transistors work in saturation region. (b) Find the minimum allowable VOUT as mentioned in (a). (c) If the channel-length modulation λn = 0.05 V-1 is considered, please calculate the IOUT when VOUT is biased at its minimum value. (d) Draw a modified circuit to cancel the error due to channel length modulation. Explain your reason. (Hint: the wide-swing current mirror shown in the textbook is one solution.) Fig. 6
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