Assignment 3 ELEC 312/Winter 12 R.Raut, Ph.D.


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1 Page 1 of 3 ELEC 312: ELECTRONICS II : ASSIGNMENT3 Department of Electrical and Computer Engineering Winter A commonemitter amplifier that can be represented by the following equivalent circuit, has C π = 10 pf, C µ = 0.5 pf, C L = 2 pf, g m = 20 ma/v, β = 100, r x = 200 Ω, R L / = 5 kω and R sig = 1 kω. Find (i) the mid band gain A M, (ii) the frequency of the zero f Z, and (iii) the approximate values of the pole frequencies f P1 and f P2. Hence estimate the 3dB frequency f H. Note that R sig is the equivalent Thevenin resistance looking towards the signal source and includes the effects of R sig, r x and r π. For approximate estimates, you may use OCTC method. + V sig / V o  (i) A M = r π (g m R L )/( R sig + r x + r π ); (ii) f Z = g m /(2π C µ ) (iii) f P1 = 1/[2π{(C π + C µ (1+ g m R L )) R sig +(C L + C µ )R L }]; f P2 = [(C π + C µ (1+ g m R L ))R sig +(C L + C µ )R L ]/[2π{C π (C L + C µ )+C L C µ )} R sig R L ]; f P1 << f P2 & f P1 << f Z, hence f H f P1 2. Analyze the highfrequency response of the CMOS amplifier shown below. The dc bias current is 100 µa. For Q 1, µ n C ox = 90 µa/v 2, V A = 12.8 V, W/L = 100 µm/1.6 µm, C gs = 0.2 pf, C gd = pf. For Q 2, C gd = pf, C gs = 36 ff and V A = 19.2 V. Assume that the resistance of the input signal generator is negligibly small. Also, for simplicity assume that the signal voltage at the gate of Q 2 is zero. Find the lowfrequency (i.e., at DC) gain, the frequency of the pole, and the frequency of the zero. You may use nodal analysis. Note: ff=1015 F, pf=1012 F. Assignment 3 ELEC 312/Winter 12 R.Raut, Ph.D.
2 Page 2 of 3 DC gain =  g m (r 01 // r 02 ), where g m = [2µ n C ox I D W/L], r 0 =V A / I D and Smallsignal gain, v o / v i = (g m sc gd1 )/[1/ r 01 +1/ r 02 +s(c L +C gd1 )] where C L = C gd2 f Z = g m /(2π C gd1 ); f p = (1/2π)[( 1/ r 01 +1/ r 02 )/(C L +C gd1 )] 3. A CG amplifier is specified to have C gs = 2 pf, C gd = 0.1 pf, C L = 2 pf, g m = 5 ma/v, χ = 0.2, R sig = 1 kω and R L / = 20 kω. Neglecting the effects of r o, find the lowfrequency gain v o / v sig, the frequencies of the poles f P1 and f P2 and hence an estimate of the 3dB frequency f H. For a CG amplifier you can use g mb = χg m. Use ac equivalent circuit. From the smallsignal equivalent circuit, v o /v i = [{1/(g m +g mb )}/{R S +1/(g m +g mb )}](g m +g mb )R L ; f p1 = 1/[2π C gs {R sig //(1/(g m +g mb ))}]; f p2 = 1/[2π(C gd +C L )R L ]. f p2 <<f p1, f p2 is the dominant pole and f H f p2 4. (a) Consider a CS amplifier having C gd = 0.2 pf, R sig = R L = 20 kω, g m =5 ma/v, C gs = 2 pf, C L (including C db ) = 1 pf, and r o = 20 kω. Find (i) the lowfrequency gain A M, and (ii) estimate f H using opencircuit time constants. Hence determine the gainbandwidth (GBW=midfreq. gain times f H ). A M = g m R L ; f H = 1/(2πτ H ) where τ H = C gs R gs + C gd R gd + C L R L, R gs = R sig, R gd = R sig (1+g m R L )+ R L ; GBW = A M f H 5. Consider the following circuit for the case: I = 200 µa and V OV = 0.25 V, R sig = 200 kω, R D = 50 kω, C gs = C gd = 1 Pf (for both transistors). Find the dc (i.e., lowfrequency) gain, the highfrequency poles, and an estimate of f H. (hint: need to find g m from I and V OV data!). V G1 = V S. [(2/g m )/((2/g m )+R S )], I = V G1 /(2/g m ), V O = IR D hence, A O = V O /V S = g m R D /(2+ g m R S ); f P1 = 1/[2π R S (C gs /2+C gd )]; f P2 = 1/(2πR D C gd ) Assignment 3 ELEC 312/Winter 12 R.Raut, Ph.D.
3 Page 1 of 5 ELEC 312: ELECTRONICS II : ASSIGNMENT4 Department of Electrical and Computer Engineering Winter (a) Consider a CS stage having C gd = 0.2 pf, R sig = 20 kω, g m =5 ma/v, C gs = 2 pf, and r o = 20 kω. (b) A CG stage is connected in totempole configuration with the CS transistor in (a) to create a cascode amplifier. The ac parameters of this stage are identical with those of the CS stage. Regarding the bodyeffect in the CG stage assume χ = 0.2. Further R L = 20 kω, and is shunted by a load capacitance C L =1 pf. Show a schematic diagram of the system using NMOS transistors. Show the ac equivalent circuit. Find (i) the lowfrequency gain AM, and (ii) estimate the gainbandwidth of the system. You may use OCTC method to determine the dominant high frequency pole f H of the system. For the cascade amplifier: AC Equivalent circuit:
4 Page 2 of 5 V gs2 = V g V s2 = 0 V s2 V bs2 = V b V s2 = 0 V s2 For low frequency gain, ignore all C gs and C gd Consider the 2 node system and derive V o / V sig + + = + + = Here = = = Using the values: v/v For Dominant role calculation, note: For C gd1, the Miller effect amplifications are : i) At input (1 + K 1 ) C gd1, K 1 = = =0.8. ii) At input (1 + C gd1 = (1+ 1.2) C gd1
5 Page 3 of 5 C gd2 does not have miller effect So the AC equivalent circuit is Ignoring r and r as was done in the class lecture. CECB Cascade The time constants are: τ 1 = = sec τ 2 =.. = sec τ 3 = sec τ 1, τ 3 are close enough,so dominant time constant principle may not apply
6 Page 4 of 5 We will take τ H = τ 1 + τ 2 + τ 3 = f H =. =. MHZ GBW = = MHZ 2. For the following circuit, let the bias be such that each transistor is operating at 100µA collector current. Let the BJTs have h fe = 200, f T = 600 MHz, and C µ = 0.2 pf, and neglect r o and r x. Also, R sig = RC = 50 kω. Show the ac equivalent circuit. Find (i) the lowfrequency gain, (ii) the highfrequency poles, and (iii) an estimate of the dominant high frequency pole f H of the system. Now find the GBW (gainbandwidth) of the system. You may use halfcircuit technique. 3. In the following circuit assume both transistors operate in saturation and λ 0. For each transistor you can assume the parasitic capacitances as C gsi, C gdi, (i=1,2).
7 Page 5 of 5 Draw the ac equivalent circuit, analyze and derive the expression for the dominant pole frequency.
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