Løsningsforslaginf34102011
Figure 1 CMOS amplifier (1) Question 1) In Figure 1 a single transistor CMOS amplifier is shown. Explain which type of single transistor amplifier this is and what is considered to be an important feature for this topology. The amplifier topology is called common‐gate amplifier. The main feature of this topology is the low input impedance provided. Question 2) Draw a small signal equivalent of the amplifier shown in Figure 1 including body‐effect and channel‐
length modulation. Question 3) Based on your small‐signal equivalent find an equation for low‐frequency transfer function and explain how body‐effect is affecting amplifier performance. Since current through is we may write 1
1
1
1
1
Vi now see gain is increase with both front gate and back gate. Figure 2 Amplifier (2) Question 4) Another amplifier is shown in Figure 2 and an application restricts maximum power consumption to 5mW. In order to ensure operation of the MOS transistor in the saturation region, output voltage should be at least 100mV above the triode region of operation for the M1 transistor. In addition the amplifier should a gain of at least 5. Find appropriate values for RD, RS and W/L You may ignore both body‐effect and channel‐length modulation and assume µnCox=200µA/V2 and Vthn=0.5V. Please note the input signal, Vin, only deliver a small input signal and is unable to provide circuit biasing. 0,005
5
⇒
4.1 1,2
100
100
1.2 Ignoring body effect and using equation 2.19 from the book: 2
KVL on output node: ⇒
2
100
2
5
1,2
5
100
2
0,5
2
2
1,2
5
0.5
100
⇒
0,66 0.5
2 ∙ 0,0041
0,66 97,5Ω ⇒
131Ω 2
1601 Figure 3 Modified amplifier Question 5) In Figure 3 a modified amplifier is shown. Again we want to ensure operation in the saturation region of the MOS transistor by biasing the M1 at least 100mV above triode region with a load current of I1=1mA. For simplicity you may ignore body‐effect and channel‐length modulation and assume the input capacitor, C1, to be fairly large. Use µnCox=200µA/V2 and Vthn=0.5V. Determine an appropriate value for the RD resistor. 1
1.2
100
Have: 100
100
100
1.2
⇒ ⇒ 0.5 1.2
0.001
0.1
400Ω Question 6) The amplifier in Figure 3 is expected to have a gain of 4. Using the RD resistor determined in Q5 and the same constants, determine an appropriate size (W/L) of the M1 transistor. 400Ω 2
4⇒
16 ⇒
256 Figure 4 Amplifier for analysis of frequency response Question 7) In the following you must account for high frequency behavior of the amplifier shown in Figure 4. As a first step to determine small‐signal frequency response, the capacitors CS and CL indicated in Figure 4 are equivalent, lumped capacitors. For each of CL and CS determine the major parasitic capacitances lumped together. Question 8) Find an equation for the transfer function of the amplifier in Figure 4 using s‐notation. Channel‐
length modulation may be ignored. Explain which pole is the dominant pole of the transfer function. Let X be the name of the source node of M1. Common gate gain: 0
KCL in X: 1
||
1
1
||
1
1 0
0 ⇒ 1
⇒ 2 1
Insert (2) in (1) 1
1
||
1
1
1
1
1