Example #7 1. The figure below shows a series-shunt amplifier with a feedback factor β=1. The amplifier is design so that vo=0 for vs=0. Use Kn’= 2Kp’=120µA/V2, |Vt|=0.7V, and |VA|=24V. (a) Ignore the early effect and find the dc currents and overdrive voltage, Vov, at which each of Q1 and Q5 is operating when Q1 gate is grounded and Q2 is at ground instead of having feedback connected its gate to the output, Vo. (b) Find gm and ro of each of the five transistors. (c) Find the expressions and values of A and Routput of the new A circuit. Assume that the bias current sources are ideal. (d) Find the gain with feedback, Af, and the output resistance Rof. (e) How would you modify the circuit to realize a closed loop gain of 5 V/V? What is the value of output resistance obtained? (a) Fall 2010 (b) 1 Example #7 (c) (d) (e) Fall 2010 2 Example #7 2. All the MOS transistors in the feedback transconductance amplifier (series (series-series) series) of the circuit below are sized to operate at |Vov|=0.2V. v|=0.2V. For all transistors |Vt|=0.4V, and |VA|=20V (a) If Vs has a zero dc component, find the dc voltage at the outp output, at the drain of Q1, and at the drain of Q2. (b) Find an approximate expression and value for Af≡ for the case ≫ 1. (c) Use feedback analysis to obtain a more precise value for Af. (d) Find the value for Rof. Fall 2010 3 Example #7 Fall 2010 4 Example #7 3. The feedback transresistance amplifier below utilizes two identical MOSFets biased by ideal current sources I=0.5mA. They are both sized to operate at Vov=0.2V and have Vt=0.5V, VA=10 10V, and RF=10kΩ. (a) If Is has a zero dc component, find the dc voltage at the input, at the drain of Q1, and at the output. (b) Find gm and ro for Q1 and Q2. (c) Find the expressions and values of A for the new A circuit in terms of gm1, ro1, gm2, ro2, and RF. (d) What is β? (e) Find the gain with feedback, Af (f) Derive expressions for Rinput and Routput of the new A circuit, and Rif and Rof for the feedback circuit. (g) Evaluate A, Aβ, Af, Rinput, Routput, Rif, and Rof for the component values given. Fall 2010 5 Example #7 4. For the amplifier circuit below assume that Vs has a zer zero dc component. Find the dc d voltages at all nodes and the dc emitter currents of Q1 and Q2. Let the BJTs have β=100.. Use feedback feedbac analysis to find Vo/Vs and Rif. Let VBE=0.7V. Fall 2010 6 Example #7 5. For the amplifier with characteri haracteristics shown in the graphs below,, what is the minimum closed-loop closed voltage gain that can be obtained for phase margins of 90o and 45o? (Assume Assume frequency-independent frequency feedback) Fall 2010 7 Example #7 6. For a multipole amplifier having a first pole at 3 MHz and a dc open-loop loop gain of 60 dB is to be compensated for closed-loop loop gains as low as unity by using additional capacitance at the circuit node at which the pole is formed to reduce the frequency of the first pole. If the e frequency of the second pole is 15MHz and if it remains unchanged while additional capacitance is introduced as mentioned, find the frequency to which the first pole must be lowered so that the resulting amplifier is stable for closed-loop closed gains as low as unity. Byy what factor is the capacitance at the controlling node increased? 7. The op amp shown below has an open open-loop gain of 105 and a single-pole rolloff olloff with ω3dB=10rad/s. (a) Sketch a Bode magnitude plot for the loop gain. (b) Find the frequency at which |Aβ β|=1 and find the corresponding phase margin. (c) Find the closed-loop loop transfer function, including its zero and poles. Sketch ketch the magnitude of the transfer function versus frequency and label the important parameters on your sketch. Fall 2010 8 Example #7 Fall 2010 9