Question 22.3: Suppose the diff-amp in Fig. 22.6 is implemented with the si......
Suppose the diff-amp in Fig. 22.6 is implemented with the sizes and bias currents seen in Table 9.1 (I_{SS} = 40\ \mu A). If the gate of M2 is held at 4 V, estimate the diff-amp’s output swing. Verify the answers with SPICE.
Table 9.1 Typical parameters for analog design using the long-channel CMOS process discussed in this book. Note that the parameters may change with temperature or drain-to-source voltage (e.g., Fig. 9.24).
Long-channel MOSFET parameters for general analog design
VDD = 5 V and a scale factor of 1 μm (scale = 1e-6)
| Parameter | NMOS | PMOS | Comments |
| Bias current, I_D | 20 \mu A | 20 \mu A | Approximate |
| W/L | 10/2 | 30/2 | Selected based on I_D\ \text{and}\ V_{DS,sat} |
| V_{DS,sat}\ \text{and}\ V_{SD,sat} | 250 mV | 250 mV | For sizes listed |
| V_{GS}\ \text{and}\ V_{SG} | 1.05 V | 1.15 V | No body effect |
| V_{THN}\ \text{and}\ V_{THP} | 800 mV | 900 mV | Typical |
| \partial V_{THN,P}/\partial T | -1\ \text{mV/C°} | -1.4\ \text{mV/C°} | Change with temperature |
| KP_n\ \text{and}\ KP_p | 120\ \mu A/V^2 | 40\ \mu A/V^2 | t_{ox}=200\ \mathring{A} |
| C_{o x}^{\prime}=\varepsilon _{o x}/t_{o x} | 1.75fF/\mu m^2 | 1.75fF/\mu m^2 | C_{ox}=C_{o x}^{\prime}WL\cdot (scale)^2 |
| C_{oxn}\ \text{and}\ C_{oxp} | 35fF | 105fF | PMOS is three times wider |
| C_{gsn}\ \text{and}\ C_{sgp} | 23.3fF | 70fF | C_{gs}=\frac{2}{3}C_{ox} |
| C_{gdn}\ \text{and}\ C_{dgp} | 2fF | 6fF | C_{gd}=CGDO\cdot W\cdot scale |
| g_{mn}\ \text{and}\ g_{mp} | 150\ \mu A/V | 150\ \mu A/V | At\ I_D=20\ \mu A |
| r_{on}\ \text{and}\ r_{op} | 5\ M\Omega | 4\ M\Omega | Approximate at I_D=20\ \mu A |
| g_{mn}r_{on}\ \text{and}\ g_{mp}r_{op} | 750 V/V | 600 V/V | Open circuit gain |
| \lambda _n\ \text{and}\ \lambda _p | 0.01\ V^{-1} | 0.0125\ V^{-1} | At L = 2 |
| f_{Tn}\ \text{and}\ f_{Tp} | 900 MHz | 300 MHz | \text{For}\ L=2,f_T\ \text{goes up if}\ L=2 |
From Eq. (22.13), the output can swing up to 4.75 V before M4 triodes. From Eq. (22.14), the output can swing down to 4-0.8 or 3.2 V before M2 triodes. The simulation results are seen in Fig. 22.7. Looking at the results, we see the output goes down to approximately 2.8 V or 400 mV less than what we predicted. This can be attributed to the body effect in M1 and M2. With body effect, the threshold voltage is 1.2 V (instead of 0.8 V).
V_{O U T M A X}=V D D-V_{S D,s a t} (22.13)
V_{D}\geq V_{G}-V_{T H N}\to V_{O U T M IN}=V_{I2}-V_{T H N} (22.14)
