Question

Problem 52: (25 points) Operational amplifiers are important building blocks in a wide spectrum of electronic systems such as amplifiers and filters. The concept of feedback control is of central importance in understanding the design of operational amplifier circuits. For without feedback, operational amplifiers behave as comparators. This problem shows why it is necessary to connect the output of an operational amplifier to its inverting input. Negative feedback produces a circuit that is BIBO stable. Figure 1(A) shows the circuit symbol for an operational amplifier, while Figure 1(B) shows an equivalent circuit model in the s-domain. Note that the input terminals are not shown connected to anything because, ideally, their input impedance is infinite (open circuit). The transfer function Ad(s) Ag has a single real pole at s -wo and a DC gain of A. Depending on the specific operational amplifier chosen, the DC gain may range from 100,000 to over 1 million, while the corner frequency wo can vary from 100 kHz to more than 1 GHz. Their product is called the gain-bandwidth product of the operational amplifier; it is one of the op-amps most important specifications. The maximum output voltage of the operational amplifier is limited by the external power supply sources, that are often called supply rails. Figure 1: Operational amplifier circuit symbol (A) and equivalent circuit (B) 1. (5 points) Using the equivalent circuit model in Figure 1(B), show that the inverting amplifier configuration in Figure 2(A) can be represented using the block diagram in Figure 2(B). Specify the value of the gains Ki and K2 in terms of R1 and R2 A,(SHV.(s) Figure 2: Inverting amplifier (A) and equivalent block diagram representation (B) 2. (5 points) Determine the transfer function representation of the block diagram representation in Figure 2(B) and place your answer in the standard form Vo(s) vi (s) sn + an-is"-1+-..+41s+40 3. (2 points) Determine if the closed-loop system represented by the transfer function in part 2 is BIBO stable. If the closed-loop system is BIBO stable, what is the DC and high frequency gain of the amplifier circuit? 4. (5 points) Using the equivalent circuit model in Figure 1(B), show that the circuit in Figure 3(A) can be represented using the block diagram in Figure 3(B). Specify the value of the gains Ki and K2 in terms of R1 and R2 s(s) A,(SHV.(s) Figure 3: Circuit (A) and equivalent block diagram representation (B) 5. (5 points) Determine the transfer function representation of the block diagram representation in Figure 3 (B) and place your answer in the standard form Vo(s) 6. (3 points) Determine if the closed-loop system represented by the transfer function in part 5 is BIBO stable. If the closed-loop system is BIBO stable, what is the DC and high frequency gain of the amplifier circuit?

Answer 1

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PAGE NO DATE These Nh() 4 2 5E6

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