Chapter 4 MOS Field-Effect Transistors (MOSFETs)
EXERCISES
1. From the description above of the operation of the MOSFET for small VDS, we note that iD is proportional to (VDS – Vt) VDS. Find the constant of proportionality for the particular device whose characteristics are depicted in Fig. 4.4. Also, give the range of drain-to –source resistances corresponding to an overdrive voltage, VGS – Vt of 0.5V to 2V.
2. Use the expression for operation in the triode region to show that an n-channel MOSFET operated in saturation with an overdrive voltage Vov =VGS-Vt and having a small VDS across it behaves approximately as a liner resistance rDS
rDS=1/[ kn´WVOV/L]
Calculate the value of rDS obtained for a device having k’n = 100A/V2 and W/L =10 when operated with an overdrive voltage of 0.5 V.
3. If the NMOS device in Exercise 4.4 has μnCox = 100μA/v2, W= 10μm, and L = 1μm, find the value of drain current that results in each of the three cases (a),(b), and (c) specified in Exercise 4.4.
4. An NMOS transistor is fabricate in a 0.4μm process having μnCox = 200μA/V2 and VA = 50 V/μm of channel length. If L= 0.8μm and W = 16μm, find VA and λ. Find the value of ID that results when the device is operated with an overdrive voltage VOV = 0.5 V and VDS = 1V. Also, find the value of r0 at this operating point. If VDS is increased by 2V, what is the corresponding change in ID?
5. An NMOS transistor has Vr0 = 0.8 V, 2φf = 0.7V, and γ=0.4V1/2. Find V1 when VSB = 3V.
D6. Redesign the circuit in Example 4.3 to double the value of ID without changing VD. Give new values for W/L and R.
7. If in the circuit of Example 4.4 the value of RD is doubled, find approximate values for ID and VD.
D8. Redesign the circuit of Fig. 4.23 for the following requirements; VDD = +5V, ID = 0.32 mA ,VS = 1.6, VD = 3.4V, with a 1-μA current through the voltage divider RG1, RG2. Assume the same MOSFET as in Example 4.5.
9. For the circuit studied in Example 4.8 above and with reference to the transfer characteristic sketched in Fig. 4.26 (c): (a) Give the values of V1Q, VIB, VOQ, and VOB. (b) Use the values in (a) to determine the largest allowable value of the negative peak of the output signal and the magnitude of the corresponding positive peak of the input signal. Disregard distortion caused by the square-law MOSFET characteristic. (c) Repeat (b) for the positive-output peak and the corresponding negative-input peak. (d) From the results of (b) and (c), what is the maximum amplitude of a sine wave that can be applied at the input and the corresponding output amplitude. What value of gain do these amplitudes imply? Why is it different from the 14.7 V/V found in Example 4,8?
10. Consider the MOSFET in Example 4.9 when fixed-VGS bias is used. Find the required value of VGS to establish a dc bias current ID = 0.5 mA. Recall that the device parameters are Vt = 1 V, k’nW/L =1mA/V2, and λ= 0. What is the percentage change in ID obtained when the transistor is replaced with another having Vt = 1.5 V?
11. It is required to design the circuit in Fig, 4.32 to operate at a dc drain current of 0.5mA. Assume VDD = + 5V, k’n W/L = 1mA/V2, Vt = 1V, and λ= 0. Use a standard 5% resistance value for RD, and give the actual values obtained for ID and VD.
12. For the amplifier in Fig. 4.34, let VDD = 5V, RD = 10 kΩ , Vt = 1V, = 20μA/V2, W/L=20, VGS=2V,λ=0. (a) Find the dc current ID and the dc voltage VD. (b) Find gm. (c) Find the voltage gain. (d) If υgs = 0.2 sinωt volts, find Vd assuming that the small-signal approximation holds. What are the minimum and maximum values of VD? (e) Use Eq.(4.57) to determine the various components of iD. Using the identity (sin2ωt = cos2ωt ), show that there is a slight shift in ID ( by how much? ) and that there is a second-harmonic component (i.e., a component with frequency 2ω). Express the amplitude of the second-harmonic component as a percentage of the amplitude of the fundamental. (This is value is known as the second-harmonic distortion.)
13. A MOSFET is to operate at ID = 0.1 mA and is to have gm = 1 mA/V. If k’n= 50μA/V2 , find the required W/L ratio and the overdrive voltage.
14. For an NMOS transistor with 2φf = 0.6V, γ= 0.5V1/2, and VSB = 4V, find χ≡ gmb/gm
15. Use the formulas in Table 4.2 to derive an expression for (gmro) in terms of VA and VOV. As we shall see in Chapter6, this is an important transistor parameter and is known as the intrinsic gain. Evaluate the value for gmro for an NMOS transistor fabricated in a 0.8-μm CMOS process for which V’A =12.5 V/μm of channel length. Let the device have minimum channel length and be operated at an overdrive voltage of 0.2V.
16. (a) If in the amplifier of Example 4.11, Esig is doubled, find the values for Rin, GV, and Rout. (b) Repeat for RL doubled (but Rsig unchanged; i.e., 100kΩ). (c) Repeat for both Rsig and RL doubled.
17. In Exercise 4.32 we applied an input signal of 0.4V peak-to-peak, which resulted in an output signal of the CS amplifier of 2.8V peak-to-peak. Assume that for some reason we now have an input signal three times as large as before (i.e.,1.2 V p-p) and that we wish to modify the circuit to keep the output signal level unchanged. What value should we use for Rs?
18. Consider a source follower such as that in Fig, 4.46 (a) designed on the basis of the circuit of Fig. 4.42, the results of whose analysis are displayed in Fig. E4.30. Specifically, note that gm = 1mA/V and γo = 150 kΩ. Let Rsig= 1 MΩ and RL = 15 kΩ. (a) Find Rin, AVO, AV, and Rout without and with γo taken into account. (b) Find the overall small-signal voltage gain GV with γo taken into account.
19. Calculate fT for the n-channel MOSFET whose capacitances were found in Exercise 4.36. Assume operation at 100μA, and k’n = 160μA/V2.
20. If it is possible to replace the MOSFET used in the amplifier in Example 4.12 with another having the same Cgs but a smaller Cgd , what is the maximum value that its Cgd can be in order to obtain an fH of at least 1 MHz?
EXAMPLES
1. Consider a process technology for which Lmin= 0.4μm,tox= 8 nm, μn =140cm2/V-s, and Vt =0.7V.
(a) Find Cox and k’n .
(b) For a MOSFET with W/L = 8μm/0.8μm, calculates the values of VGS and VDSmin needed to operate the transistor in the saturation region with a dc current ID =100μA .
(c) For the device in (b), find the value of VGS required cause the device to operate as a 1000-Ω resistor for very small VDS
2. Design the circuit in Fig. 4.21 to obtain a current ID of 80μA. Find the required for R, and find the dc voltage VD. Let the NMOS transistor have Vt =0.6V, μnCox =200μA/V2 , L= 0.8μm, and W =4μm. Neglect the channel-length modulation effect (i.e., assume λ=0)
3. Analyze the circuit shown in Fig. 4.23(a) to determine the voltages at all nodes and the currents through all branches. Let Vt =1 V and k’n(W/L) =1mA/V2 . Neglect the channel-length modulation effect (i.e., assume λ=0)
4. The NMOS and PMOS transistor in the circuit of in Fig. 4.25(a) are matched with k’n(Wn/Ln) =1mA/V2 and Vtn = -Vtp =1 V. Assumingλ=0 for both devices, find the drain currents iDN and iDp , as well as the voltage Vo, for Vi = 0V, +2.5, and -2.5V .
5. It is required to design the circuit of Fig. 4.30(c) to establish a dc drain current ID = 0.5mA. The MOSFET is specified to have Vt =1 V and k’n(W/L) =1mA/V2 .For simplicity, neglect the channel-length modulation effect (i.e., assume λ=0). Use a power-supply VDD = 15V. Calculate the percentage change in the value of ID obtained when the MOSFET is replaced with another unit having the same k’n(W/L) but Vt =1.5V
6. A transistor amplifier is fed with a signal source having an open- circuit voltage Vsig of 10mV and an internal resistance Rsig of 100KΩ. The voltage Vi at the amplifier input and the output voltage Vo are measured both without and with a load resistance RL = 10 KΩ connected to the amplifier output. The measured results are as follows:
Find all the amplifier parameters.
7. We wish to select appropriate values for the coupling capacitors Cc1 and Cc2 and the bypass capacitor Cs for the CS amplifier whose high-frequency response was analyzed in Example 4.12. the amplifier has RG = 4.7 MΩ, RD=RL = 15 KΩ, Rsig = 100 KΩ, and gm = 1mA/V . It is required to have fL at 100Hz and that the earest break frequency be at least a decade lower.
Chapter 6 Single-Stage Integrated-Circuit Amplifiers
EXERCISES
1.(a) For NOMS transistor in the 0.18μm technology in Table 6.1, find the range of obtained for VOV ranging from 0.2V to 0.4V and W/L =0.1 to100. Neglect channel length modulation. (b) If a similar range of current is required in an npn transistor fabricated in the low voltage process specified in Table 6.1, find the corresponding change in its VBE.
2. Find ID $, gm , ro , Cgd , and fT for an NOMS transistor fabricated in the
0.5μm COMS technology specified in Table 6.1. Let L= 0.5μm, W=5μm, and VOV = 0.3V.
3. For the circuit of Fig.6.7,let VDD=VSS=1.5V,Vtn= 0.6V, Vtp= -0.6V,all channel lengths=1μm, k’n=200μA/V2, and λ=0. For IREF=10μA,find the widths of all transistors to obtain I2= 60μA,I3 = 20μA,and I5 = 80μA.It is further required that the voltage at the drain of Q2 be allowed to go within 0.2V of the negative supply and that the voltage at the drain of Q5 be allowed to go up to within 0.2V of the positive supply and that the voltage at the drain of Q5 be allowed to go up to within 0.2V of the positive supply.
D4.Assuming the availability of BJTs with scale currents IS=10-15A , β=100,and VA=50V, design the current-source circuit of Fig.6.10 to provide an output current IO=0.5mA at VO=2V.The power supply VCC=5V.Given the values of IREF , R , and VOmin. Also , find I0 at VO=5V.
5. A direct-coupled amplifier has a dc gain of 1000V/V and an upper 3-dB frequency of 100 KHz. Find the transfer function and the gain-bandwidth product in hertz.
6. For the amplifier described in Exercise 6.10, find the exact and approximate values (using Eq.6.36) of ωH (as a function of ωp1 ) for the case k= 1 , 2 , and 4.
7. Use Miller’s theorem to investigate the performance of the inverting op-amp circuit shown in Fig.E6.13.Assume the op amp to be ideal except for having a finite differential gain , A. Without using any knowledge of op-amp circuit analysis , find Rin ,Vi , VO, and Vo/ Vsig ,for each of the following values of A:10V/V , 100V/100V , and 10,000V/V . Assume Vsig=1V.
8. A CMOS common-source amplifier fabricated in a 0.18μm technology has W/L=72μm/0.36μm for all transistors, k’n = 387μA/V2, k’p= 86μA/V2 , IREF=100μA,V’An=5V/μm , and |VAP| = 6V/μm . Find gm1 , ro1 , ro2 , and the voltage gain.
9. For the CS amplifier in Example 6.9, using the value of fH determined by the exact analysis, find the gain-bandwidth product . Also, convince yourself that is the frequency at witch the gain magnitude reduces to unity.
10. As another way to trade dc gain for bandwidth, the designer of the CS amplifier in Example 6.9 decides to operate the amplifying transistor at double the value of VOV by increasing the bias current fourfold (i.e., to 400μA) . Find the new values of gm, R’L , |AM| , fP1 , fH , and ft .Use the approximate formula for fP1 given in Eq.(6.66).
11. For the CS amplifier considered in Example 6.10 operating at the original values of VOV and ID (i.e., VOV= 0.16V and ID= 100μA) , find the value to which CL should be increased to place ft at 2GHz.
12. For the CG amplifier considered in Example 6.11, find the value of fH when a capacitance CL = 5fF is connected at the output.
13. Consider the CB amplifier of Fig. 6.33 (a) for the case I=1mA, β=100, VA=100V. RL=1MΩ, and Re = 1KΩ.Find Rin , AVO , RO , AV , Rout , and GV. Also, find VO if is a 5-mV peak sine wave.
Examples
1.(a) For an NMOS transistor with W/L =10 fabricates in the 0.18-μm process whose data are given in Table 6.1, find the values of VOV and VGS required to operate the device at ID =100μA . Ignore channel-length modulation.
(b) Find VBE for an npn transistor fabricated in the low-voltage process specified in Table 6.2 and operate at Ic = 100μA. Ignore base –width modulation.
2. In this example we investigate the gain and the high-frequency response of an npn transistor and an NMOS transistor. For the npn transistor, assume that it is fabricated in the low-voltage process specified in Table 6.2,and assume that Cμ Cμo. For Ic = 10μA, 100μA, and 1mA, find gm, ro , Ao , Cde, Cje, CΠ, Cμ , fT. Also, for each value of Ic , find the gain-bandwidth product ft of a common-emitter transistor loaded a 1-pF capacitance, neglecting the internal capacitances of transistor. For the NMOS transistor, assume that it is fabricated in the 0.25-μm process with L= 0.4μm. Let the transistor be operated at VOV =0.25V. Find W/L that is requires to ID = 10μA, 100μA, and 1mA. At each values of ID ,find gm, ro, Ao , Cde, Cje, CΠ, Cμ , fT. Also, for each value of ID , determine the gain-bandwidth product ft of a common-source transistor loaded by a 1-pF capacitance, neglecting the internal capacitances of the transistor.
3. The high-frequency response of an amplifier is characterized by the transfer function
Determine the 3-dB frequency approximately and exactly.
4. Fig. 6.16(a) shows an ideal voltage amplifier having a gain of -100V/V with an impedance Z connected between is output and input terminals. Find the Miller equivalent circuit when Z is
(a) a 1MΩ resistance, and (b) 1pF capacitance. In each case, use the equivalent circuit to determine Vo/Vsig .