EJECICIOS DE COMPONENTES ELECTÓNICOS. 1 er cuatrimestre 2 o Ingeniería Electrónica Industrial Juan Antonio Jiménez Tejada Índice 1. Basic concepts of Electronics 1 2. Passive components 1 3. Semiconductors. Basic concepts. 1 4. Circuit simulation tools. SPICE. 1 5. Semiconductors. I-V characteristic of a semiconductor. 2 6. Semiconductors. The PN junction 2 7. Diodes 3 8. The Bipolar Junction Transistor (BJT) 8 9. The Metal Oxide Semiconductor Field Effect Transistor (MOSFET) 12 i
1. Basic concepts of Electronics Exercise 1 Consider the following voltage signal v A (t) = 5 10 3 +3cos(2π10 3 t+π/4) mv. Write the values or expressions for the dc voltage, ac voltage, total voltage, amplitude of the ac voltage, phasor of the ac signal, root mean square of the ac signal and frequency of the ac signal. 2. Passive components Exercise 2 a) Generate series of numbers of 3, 6, 12, 24, 48, 96 and 192 values between 1 and 10 equally spaced in a logarithmic scale. b) Consider the case with 24 elements. Determine the relative error between two consecutive values. Compare the results with the series of resistances with 5% tolerance. 3. Semiconductors. Basic concepts. Exercise 3 The intrinsic carrier concentration in a semiconductor is a function of the temperature T: n i = BT 3/2 exp[ E G /(2KT)]. Find the value of B for silicon, germanium and gallium arsenide. Use the tables with the properties of the semiconductors. Exercise 4 Using the result of the Problem 3, find the value of the intrinsic carrier concentration for the silicon at 50 and 350 K. Exercise 5 A silicon semiconductor is doped with donor impurities in concentration 2 10 17 cm 3. Find the concentration in equilibrium of electrons and holes at 50, 300 and 350 K. Assume that all the impurities are ionized at the three temperatures. 4. Circuit simulation tools. SPICE. Exercise 6 Analyze in Pspice the circuit of Figure 1. (a) epresent in Pspice v i and v as a function of the time. When you define the simulation profile, select Time domain(transient) in the Analysis type menu. Write an appropriate time range in un to time in order to see three periods of the signal (3T). Select a maximum step size equal to T/500. Write 0 seconds after the option Start saving data after. (b) Observe what happens when you write the value of the period T after Start saving data after, instead of 0 seconds. (c) Add a new trace in the results window: v i v. (d) Copy the data of v i and v into Excel or other similar application. epresent the data in a figure. Write the title and magnitudes in the axes with their units. Data: v i = 5cos(2π100t) mv, =1KΩ, C=1 µf Figure 1: 1
5. Semiconductors. I-V characteristic of a semiconductor. Exercise 7 A uniform bar of p-type silicon of 1 µm length and 0.1 µm 2 cross sectional area has a voltage of 5 V applied across it. The dopant concentration is 5 10 16 cm 3. (a) Find the majorityand minority-carrier drift-velocities, (b) the time the majority and minority carriers take to cross the 1 µm bar, (c) the drift-current density and its components for electrons and holes, and (d) the drift current. Exercise 8 In the shaded region of the semiconductor device of the Figure 2 the hole concentration profile is p(x) = p 0 exp( x/l p ) with L p = 1µm and the value of the concentration of holes at x = 0 is p 0 = p(0) = 2 10 16 cm 3. If the cross sectional area of the device is A = 100µm 2, find the hole current density and the hole current at x = 0. If W = 10µm, find the value of p(w). Figure 2: Exercise 9 In the shaded region of the semiconductor device of the Figure 3(a) the hole concentration profile is shown in Figure 3(b) with p 0 = 2 10 16. Find the hole current density and the hole current in the shaded region. Data: cross sectional area A = 100µm 2 and W = 1µm. Figure 3: 6. Semiconductors. The PN junction Exercise 10 Consider a silicon PN junction in equilibrium at 200 K with the following parameters: P region: length L P = 200 nm, concentration of acceptor impurities 10 18 cm 3. N region: length L N = 200 nm, concentration of donor impurities 10 17 cm 3. 2
(a) Determine the value of the built-in voltage (or barrier voltage). (b) Determine the values of the width of the depletion region (also named space charge region) in both the N and P regions of the junction. Indicate these widths in the following representation. (c) epresent in a figure with logarithmic scale the concentration of electrons and holes along the whole PN junction (range for the x-axis x [ 200, 200] nm). (d) Determine and represent in another figure the charge density along the PN junction. In this figure, write the name of the different regions of the PN junction: depletion or neutral regions. Exercise 11 Consider the silicon PN junction of Exercise 10 at 200 K. (a) Determine the values of the width of the depletion region in both the N and P regions of the junction in the following situations: i) reverse bias (V = V = 5 V) and forward bias (V = V F = 0.6 V). (b) In these two cases, evaluate the concentration of holes at the N-border of the depletion region p n (x n ). (c) In these two cases, evaluate the concentration of electrons at the P-border of the depletion region n p ( x p ). Exercise 12 (a) Determine the value of the saturation current for the pn junction of Exercise 10 at 200 and 300 K. (Data: diffusion length for electrons 10 µm, diffusion length for holes 10 µm, cross sectional area A = 100µm 2 ). (b) At V = 0.62 V and 300 K, determine the value of the current along the PN junction. Determine the value of the contributions of the electrons and holes to the total current. (c) At V = 0.62 V and 300 K, determine the values of the charge of minority carriers stored in the neutral regions of the N and P sides of the PN junction. (d) At V = 0.62 V and 300 K, determine the values of the hole and electron lifetimes. Estimate the value of the mean transit time. (e) At V = 0.62 V and 300 K, determine the value of the incremental diffusion capacitance. Exercise 13 Pspice models the depletion capacitance C j of a PN junction with three parameters (CJO, VJO and MJO) reading: CJO C j = ( ) 1+ V MJO (1) VJO where V is the reverse bias applied to the junction. (a) Determine the value of these three parameters for the PN junction of Exercise 10 at 300 K. (b) Determine the value of the depletion capacitance at V = 5 V. (c) Determine the value of the depletion capacitance at V = 0.62 V (forward bias). (d) To avoid calculation problems at V VJO, a linear approximation is used under forward bias to estimate the depletion capacitance: C j = MJO CJO V VJO +CJO where the slope of this function coincides with the slope of (1) at V = 0. Determine the value of the depletion capacitance at V = 0.62 V using this new approximation. Compare this value with the value of the incremental diffusion capacitance obtained in Exercise 12(e). 7. Diodes Exercise 14 Find and represent the transfer characteristic V o V i of the three circuits of Figure 4. Hint: In the first place, find the value of V i at which the diode starts to be in the conduction state (at this point, impose V d = V γ = 0.6 V and I d = 0). Use the Kirchhoff s current law applied at node V o. 3
Figure 4: Exercise 15 Find the maximum value of v A in the circuit of Figure 5 in order to apply the small signal model of the diode. For this voltage, find the expression of the total voltage drop at the diode v D (t). Use the superposition principle and the large and small signal models of the diode to analyze the dc and ac signals, respectively. Figure 5: Exercise 16 Consider a diode biased at 2 ma. Find the change in current as a result of changing the voltage by (a) +2.58 mv and (b) -2.58 mv. (i) Use the small signal model. (ii) Use the exponential model. Determine the relative error. Exercise 17 Consider the voltage regulator circuit shown in Figure 6(a). The value of is selected to obtain an output voltage across the diode V o = 0.65 V. Data: the saturation current of the diode is 10 14 A and V CC = 12 V. (a) Use the small signal model to show that the change in output voltage corresponding to a change of V CC in V CC [Figure 6(b)] is V o V CC = VT V CC +VT 0.65 This quantity is known as the line regulation and is usually expressed in mv/v. Evaluate this expression. V T is the thermal voltage. (b) Now, a current I L is drawn from the output terminal [Figure 6(c)]. If the value of I L is sufficiently small so that the corresponding change in the regulator output voltage is small enough to justify using the small-signal model, show that V o I L = r d // = r d V CC 0.65 V CC 0.65+VT This quantity is known as the load regulation and is usually expressed in mv/ma. Evaluate this expression. 4
Figure 6: Exercise 18 (a) Design a shunt regulator of approximately 20 V. There are two kinds of zener diodes in the laboratory: 6.8 V devices with r z = 10Ω and 5.1 V devices with r z = 30Ω. For the two major choices possible, find the load regulation. In the calculation neglect the effect of the regulator resistance. (The name of shunt regulator comes from the fact that the regulator system appears in parallel (shunt) with the load). (b) Show that the minimum value of the resistance we can use as a load in the circuit is Lmin = nv z0 V CC nv z0 Evaluate this expression for the two designs in (a) assuming a voltage supply V CC = 35 V and a regulator resistance = 2 KΩ. Exercise 19 Find and represent the transfer characteristic V O V i for the circuit of Figure 7. Figure 7: Exercise 20 In the rectifier of Figure 8, v S = 10sin(ωt+φ) V and = 1 KΩ. Find (a) the value of the angle ωt+φ at which the diodes start to conduct, (b) the fraction (percentage) of each cycle during which v O > 0, (c) the maximum value of v O, (d) the peak diode current, (e) the average value (dc component) of v O and (f) the value of the peak inverse voltage (PIV). Figure 8: Exercise 21 In the rectifier of Figure 9, v S = 10sin(ωt+φ) V and = 1 KΩ. Find (a) the value of the angle ωt+φ at which the diodes start to conduct, (b) the fraction (percentage) of each cycle during which v O > 0, (c) the maximum value of v O, (d) the peak diode current, (e) the average value (dc component) of v O and (f) the value of the peak inverse voltage (PIV). 5
Figure 9: Exercise 22 In the rectifier of Figure 10, v S = 10sin(ωt+φ) V and = 1 KΩ. Find the value of the capacitance to obtain a peak-to-peak ripple voltage of (i) 10% of the peak output and (ii) 1% of the peak output. In each case, (a) What average output voltage results? (b) What average current flows across the resistance? (c) What fraction of the cycle does the diode conduct? (d) Estimate the average diode current during conduction by assuming, during this time interval, that the current flowing across the resistance is negligible. Also, consider that the charge injected into the capacitor during the OFF interval must be extracted during the ON interval. (e) Estimate the peak diode current from the previous value. (f) Determine the peak diode current with i Dmax = i (1+2π 2V p /V r ) Figure 10: Exercise 23 In the rectifier of Figure 11, v S = 10sin(ωt+φ) V and = 1 KΩ. Find the value of the capacitance to obtain a peak-to-peak ripple voltage of (i) 10% of the peak output and (ii) 1% of the peak output. In each case, (a) What average output voltage results? (b) What average current flows across the resistance? (c) What fraction of the cycle does the diode conduct? (d) Estimate the average diode current during conduction by assuming, during this time interval, that the current flowing across the resistance is negligible. Also, consider that the charge injected into the capacitor during the OFF interval must be extracted during the ON interval. (e) Estimate the peak diode current from the previous value. (f) Determine the peak diode current with i Dmax = i [1+2π V p /(2V r )] Exercise 24 Consider the circuits of the Figures 12(a)-(d). The input voltage v i (t) is represented in Figure (e). Find the output voltage in each circuit (v o (t), v o (t), v o (t) and v o (t), respectively). Hint for circuit (d): analyze the circuit in two stages, combining the results of the circuits (c) and (a). First, obtain v o(t) as in circuit (c). Second, analyze the rest of the circuit as in Figure 6
Figure 11: (a). The circuit of Figure (d) is known as voltage doubler. The reason is that for a symmetric input (V 2 = V 1 ) the output is v o (t) = 2V 1 +2V γ. Data: V 1 = 2 V, V 2 = 3 V, V γ = 0.7 V. Figure 12: Exercise 25 In the circuit of Figure 13, the input voltage is a square signal changing between V imax = +6 and V imin = 6 V. The circuit works under permanent periodic regime with period T. Assume that C T. What does this condition mean? How does this condition affect the analysis of the circuit? Once these questions are answered, find the values of V o for V i = V imax and V i = V imin. epresent in the same figure the input and output signals as a function of the time. C + T/2 Vi 6V + Vi - Vo t - T -6V Figure 13: Exercise 26 In the circuit of Figure 14, the input voltage is a square signal changing between V imax = +5 and V imin = 5 V. The circuit works under permanent periodic regime with period T. Assume that C T. Find the values of V o for V i = V imax and V i = V imin. epresent in the same figure the input and output signals as a function of the time. 7
Figure 14: Exercise 27 Find and represent the transfer characteristic V O V i for the circuit of Figure 15. ( 1 = 3KΩ, 2 = 1KΩ). Figure 15: 8. The Bipolar Junction Transistor (BJT) Exercise 28 Consider a silicon bipolar transistor with the following features: area A=0.0014 cm 2, width of the base region 1 µm, electron diffusion coefficient 18 cm 2 /s, hole diffusion coefficient 10 cm 2 /s. region impurities concentration emitter donors 10 19 cm 3 base acceptors 10 17 cm 3 collector donors 10 16 cm 3 1. Find the value of the collector current of the transistor operating in the active region at V BE = 0.65 V and V BC = 5 V. 2. Find the value of the width of the depletion region of the base-emitter junction. Find the value of the width of this depletion region inside the base region? 3. Find the value of the width of the depletion region of the base-collector junction. Find the value of the width of this depletion region inside the base region? 4. What is the effective width of the base region (defined as the width of the base region minus the widths of the depletion regions inside the base)? Exercise 29 Consider the BJT of exercise 28 in saturation at i) V BE = 0.65 V, V BC = 0.55 V and ii) V BE = 0.65 V, V BC = 0.6 V. a) Find the value of the concentration of the minority carriers at the edges of the depletion regions of the BE and BC junctions (only in the base region). b) Estimate the value of the collector current by calculating the diffusion current in the base region. 8
Exercise 30 Consider the BJT of exercise 28 in the active region at i) V BE = 0.65 V, V CE = 0.4 V and ii) V BE = 0.65 V, V CE = 5.65 V. The objective of this exercise is to analyze the Early effect. 1. Find the value of the width of the depletion region of the base-emitter junction. Find the value of the width of this depletion region inside the base region? 2. Find the value of the width of the depletion region of the base-collector junction. Find the value of the width of this depletion region inside the base region? 3. Find the value of the effective width of the base region. 4. Find the value of the collector current using the value of the effective width of the base region. 5. Using the values of the current evaluated at V CE = 0.4 V and V CE = 5.65 V, find the value of the Early voltage V A. Exercise 31 Consider the circuit of Figure 16. Find the values of V CE and I C for the cases (a) V BB = 2 V, (b) V BB = 1 V and (c) V BB = 0.6 V. Data: β = 150, V γ = 0.7 V, V CC = 12 V, C = 2 KΩ, B = 30 KΩ. Figure 16: Figure 17: Exercise 32 Consider the circuit of Figure 17. Find the values of V EC and I C for the cases (a) V BB = 5 V, (b) V BB = 2 V and (c) V BB = 0.6 V. Data: β = 50, V γ = 0.7 V, V CC = 12 V, C = 2 KΩ, B = 30 KΩ. Exercise 33 In the circuit of Figure 18, assume that the transistor operates in the active region at V BE = 0.65 and 0.69 V. Find the transfer characteristic between the output voltage v O and the input voltage v i. Find the value of the collector current and the voltage v O if I S = 10 14 A. Find the value of the derivative dv o /dv i at v i = 0.65 and 0.69 V. Figure 18: 9
Figure 19: Figure 20: Exercise 34 Consider the circuit of Figure 16. A signal v s with a small amplitude has been added in series with V BB, as shown in Figure 19. Only one of the three cases of Figure 16 can operate as amplifier. Choose it. (a) Find the values of the following parameters of the small-signal model of the BJT: transconductance, input resistance at the base, input resistance at the emitter. (b) Using the small signal model, find the value of the voltage gain v o /v i. Exercise 35 Consider the circuit of Figure 17. A signal v s with a small amplitude has been added in series with V BB, as shown in Figure 20. Only one of the three cases of Figure 17 can operate as amplifier. Choose it. (a) Find the values of the following parameters of the small-signal model of the BJT: transconductance, input resistance at the base, input resistance at the emitter. (b) Using the small signal model, find the value of the voltage gain v o /v i. Exercise 36 Find the bias point (I C, V CE ) of each circuit shown in Figure 21. Data: (a) V CC = 12 V, 1 = 52.75 KΩ, 2 = 70.16 KΩ, C = 2 KΩ, E = 5.97 KΩ, β = 200, V γ = 0.7 V. (b) V CC = 12 V, V EE = 12 V, B = 250 KΩ, C = 2 KΩ, E = 10 KΩ, β = 200, V γ = 0.7 V. (c) V CC = 12 V, B = 1.86 MΩ, C = 2 KΩ, β = 200, V γ = 0.7 V. (d) V CC = 12 V, V EE = 12 V, B = 250 KΩ, C = 2 KΩ, β = 200, V γ = 0.7 V, I = 1 ma. Figure 21: 10
Exercise 37 In the Figure 25, four amplifier configurations with BJT are shown: (a) the common emitter amplifier, (b) the common base amplifier, (c) the common collector amplifier (also known as emitter follower) and (d) the common emitter amplifier with emitter resistance. The bias circuits are not shown, only the small-signal generators V s are seen in the circuits. Assuming that all the transistors are biased in the active region at I C = 1 ma, determine the expressions and values of the voltage gain A v = V o /V i, the input resistance i and the output resistance o in each circuit. Consider two cases: 1. Neglect the Early effect. 2. V A = 50 V. Data: S = 1 KΩ, C = 5 KΩ, E = 0.5 KΩ. Figure 22: Exercise 38 In the circuit of Figure 23, determine the value of the following variables: The DC current and voltage at each terminal of the transistor. The parameters of the small-signal model of the transistor. The open-circuit voltage gain A vo. The voltage gain A v = v o /v i. The overall voltage gain G v = v o /v s. The input resistance i. The output resistance o. The maximum and minimum allowable voltage swings of the output signal v o (t) (if possible). (Advice: employ the T model). Exercise 39 In the circuit of Figure 24, determine the value of the following variables: The DC current and voltage at each terminal of the transistor. The parameters of the small-signal model of the transistor. The open-circuit voltage gain A vo. The voltage gain A v = v o /v i. The overall voltage gain G v = v o /v s. The input resistance i. The output resistance o. The maximum and minimum allowable voltage swings of the output signal v o (t) (if possible). (Advice: employ the T model). 11
Vcc I=1 ma B=200 k C O S=1 k i V o V i C L=20 k V S E=225 =100 V =0.7 V BE Figure 23: =100 V =0.7 V BE Vcc I=0.8 ma C O B=200 k V o C E= 125 i V i L=20 k S=0.1 k V S Figure 24: Exercise 40 Design the current source of the circuit of Figure 24. Use the current mirror of Figure 25 and find the value of. With this design, find the value of the maximum allowable voltage swing of the output signal v o (t) in circuit of Figure 24. Hint: Q3 must remain in the active region. Figure 25: 9. The Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Exercise 41 Find the value of the drain current in an n-channelmosfet at a) V DS = 3 V, V GS = 2 V, b) V DS = 0.5 V, V GS = 2 V and c) V DS = 2 V, V GS = 0.5 V. Data: threshold voltage, 1 V; process transconductance parameter, 0.5 ma/v 2 ; channel length, 1µm; transistor width, 10 µm. 12
Exercise 42 Find the value of the drain current in a p-channel MOSFET at a) V SD = 2 V, V SG = 3 V, b) V SD = 1 V, V SG = 3 V and c) V SD = 2 V, V SG = 0.5 V. Data: threshold voltage, -0.8 V; process transconductance parameter, 0.5 ma/v 2 ; channel length, 1µm; transistor width, 10 µm. Exercise 43 In the circuit of Figure 26, a) Find the values of v DS and v GS at the limit between the saturation and triode regions. Find the value of v DS at b) v GS = 0.3 V, c) v GS = 1 V, d) v GS = 3.5 V. Find the slope of the relation v DS v GS at v GS = 1 V. Data: threshold voltage, 0.5 V; process transconductance parameter, 0.5 ma/v 2 ; channel length, 1µm; transistor width, 10µm; D = 2 KΩ; V DD = 3 V. Figure 26: Exercise 44 Consider the circuit of Figure 27. Using the small signal model, find the value of the voltage gain v ds /v gs for the following three cases: a) V GS = 0.3 V, b) V GS = 1 V, c) V GS = 3.5 V. Data: threshold voltage, 0.5 V; process transconductance parameter, 0.5 ma/v 2 ; channel length, 1µm; transistor width, 10µm; D = 2 KΩ; V DD = 3 V. Figure 27: Exercise 45 In the Figure 28, four amplifier configurations with MOSFET are shown: (a) the common source amplifier, (b) the common source amplifier with a source resistance, (c) the common gate amplifier and (d) the common drain amplifier (also known as source follower). The bias circuits are not shown, only the small-signal generators V s are seen in the circuits. Assuming that all the transistors are biased in the saturation region at I D = 1 ma, determine the expressions and values of the voltage gain A v = V o /V i, the input resistance i and the output resistance o in each circuit. Consider two cases: 1. Neglect the Early effect. 2. V A = 50 V. 13
Data: S = 1 KΩ, D = L = 5 KΩ, SS = 2 KΩ, MOSFET transconductance parameter = 0.5 ma/v 2. Figure 28: Exercise 46 Find the bias point (I D, V DS ) of the transistor Q3 in each circuit shown in Figure 29. Data: (a) V DD = 5 V, V SS = 5 V, D = 5 KΩ, G = 10 MΩ, = 7.42 KΩ. K n = 0.8mA/V 2, V th = 1 V and V A = 40 V for all the transistors. Neglect the Early effect. (b) V DD = 5 V, V SS = 5 V, D = 5 KΩ, G = 10 MΩ, S = 2.42 KΩ, K n = 0.8mA/V 2, V th = 1 V, V A = 40 V. Neglect the Early effect. (c) V DD = 5 V, V SS = 5 V, D = 4 KΩ, 1 = 8 MΩ, 2 = 2 MΩ, S = 3.42 KΩ, K n = 0.8mA/V 2, V th = 1 V, V A = 40 V. Neglect the Early effect. (d) V DD = 5 V, D = 2.42 KΩ, G = 10 MΩ, K n = 0.8mA/V 2, V th = 1 V, V A = 40 V. Neglect the Early effect. Exercise 47 Consider the amplifier with MOSFET of the Figure 30. The input signal is v sig = 500sinωt mv. Determine and represent as a function of the time the signal v o (t). Indicate all the intermediate steps needed to determine this signal. In particular, determine the value of the opencircuit voltage-gain, A vo, the voltage-gain Av = v o /v i, the overall voltage-gain, G v = v o /v sig, the input resistance in and the output resistance out. Data: V DD = 5 V, D = 2.42 KΩ, G = 10 MΩ, L = 40 KΩ, sig = 1 KΩ, K n = 0.8mA/V 2, V th = 1 V, V A = 40 V. Neglect the Early effect in the DC calculation. Exercise 48 Consider an n-channel MOSFET with the following parameters and dimensions: width, 0.9 µm; channel length, 0.18 µm; oxide thickness, 5 nm; threshold voltage, 0.9 V. Find the values of the oxide capacitance, the oxide capacitance per unit area, the process transconductance parameter and the MOSFET transconductance parameter. If the transistor operates at v GS = 5 V and at a low values of v DS, find the value of the electron charge in the channel. If v DS = 0.1 V, find the value of the electric field in the channel and the electron drift-velocity. 14
Figure 29: Figure 30: Exercise 49 In an n-channel MOSFET with threshold voltage, 0.9 V, the following two measurements have been taken at v GS = 5 V: I D = 44.3 ma at v DS = 7 V and I D = 48 ma at v DS = 15 V. Find the Early voltage. Exercise 50 a) Find the bias point (I D1, V DS1, V S1, V B1 ) of the transistor Q1 in the circuit shown in Figure 31(a). b) Find the fabrication process parameter of the transistors. Find the value of the threshold voltage of the transistor Q2 assuming that V SB2 = V S2 V B2 = V S1 V B2, where V B2 = 12 V. With this value of the threshold voltage, find the bias point (I D2, V DS2, V S2, V B2 ) of the transistor Q2 in the circuit shown in Figure 31(b). ecalculate the value of the threshold voltage of the transistor Q2 with the new value of V SB2 = V S2 V B2. epeat the calculation of the bias point for the transistor Q2. Do you need more iterations to find the exact bias point of Q2? Data: V DD = 5 V, V SS = 5 V, D = 5 KΩ, G = 10 MΩ, S = 2.42 KΩ, K n = 0.8mA/V 2, V th = 1 V, concentration of acceptor impurities in the n-semiconductor 10 16, W/L = 10. Exercise 51 The transistors of Figure 51 have been fabricated under the same technological process. The process transconductance parameter is 0.01 ma/v 2 and the threshold voltage is 1.2 V. The transistors Q1 and Q2 have aspect ratios of W 1 /L 1 = 100 and W 2 /L 2 = 10, respectively. 15
Figure 31: 1. Find the values of the MOSFET transconductance parameter in the two transistors. 2. Assuming that v i = 0 and Q1 operates in saturation, find an expression that relates v A with V GG. Which is the range of values of V GG that makes Q1 to operate in saturation? 3. Find the value of the voltage gain v O /v i if V GG = 1.5 V, V DD = 5 V and L = 100 KΩ. 16