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eeet-221/_Homework/hw4.md

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Skyler MacDougall

Homework 4: Due 2/10/2020

  1. Given the circuit below: hw4q9

    1. Determine the noise gain (K_n) for the circuit. K_n={1\over \beta};\ \beta={R_i\over R_i+R_f}\ K_n={68k\Omega+2k\Omega\over2k\Omega}\ \overline{\underline{|K_n=35|}}

    2. Use the result to calculate the exact signal gain at DC and low frequencies if A_o=10^5. K_n={1\over \beta};\ \beta={1\over 35}\ A_{CL}={A_o\over1+A_o\beta}={10^5\over1+(10^5)({1\over35})}\ \overline{\underline{|A_{CL}=3.9998\approx4|}}

  2. Given the circuit below:

    1. Determine the noise gain (K_n) for the circuit. K_n={1\over\beta};\ \beta={R_i\over R_i+R_f};\ R_i=12k\Omega||24k\Omega=8k\Omega\ K_n={8k\Omega+120k\Omega\over8k\Omega}\ \overline{\underline{|K_n=16|}}

    2. Use the result to calculate the exact gain factors for the two signals if A_o=5\times 10^4. K_n={1\over \beta};\ \beta={1\over 16}\ A_{CL}={A_o\over1+A_o\beta}={5\times10^4\over1+(5\times10^4)({1\over16})}\ \overline{\underline{|A_{CL}=15.9949\approx16|}}

  3. For the circuit shown in problem 9, assume the following: V_{io}=1.2mV\ I_b=60nA\ I_{io}=8nA

    1. Determine the magnitude of the output DC voltage |V_{o1}| produced by the input offset voltage. V_{o1}=V_{io}(\alpha);\ \alpha={R_f\over R_i+R_f}={34\over35}\ V_{o1}=1.2mV({34\over35})\ \overline{\underline{|V_{o1}=1.6mV|}}

    2. With R_c=0 determine the magnitude of the output dc voltage |V_{o2}| produced by the input bias currents. V_{o2}=R_c(\alpha)i_b^+-R_f(I_b^2);\ R_c=0\ i_{io}=i_b^+-i_b^-;\ i_b={i_b^++i_b^-\over2}\ 8nA=i_b^+-i_b^-;\ 120nA=i_b^++i_b^-\ i_b^+=64nA;\ i_b^-=56nA\[16pt] V_{o2}=0-68k\Omega(56nA)\ \overline{\underline{|V_{o2}=-3.808mV|}}

    3. Determine the optimum value of R_c. R_{c_{ideal}}=2k\Omega||68k\Omega\ \overline{\underline{|R_{c_{ideal}}=1.94k\Omega|}}

    4. Given your new value for R_c, find |V_{o2}|. V_{o2}=R_c(\alpha)i_b^+-R_f(I_b^2);\ R_c=0;\ i_b^+=64nA;\ i_b^-=56nA\ V_{o2}=1.94k\Omega({34\over35})(64nA)-3.808mV\ \overline{\underline{|V_{o2}=-3.688V|}}

  4. An op-amp is used at DC and very low frequencies. A closed loop gain of 200 is required. Specifications indicate that the error due to finite open loop gain cannot exceed 0.1%. Determine the minimum value of the DC open loop gain required.

I am unsure how to do this problem. It feels like there is not enough information do this problem, but I can’t seem to wrap my head around it.

  1. Assume the design of problem 25, with the following additional parameters: DC\ output\ due\ to\ input\ offset\ voltage \le100mV\ DC\ output\ due\ to\ input\ offset\ current \le5mV\

    1. Determine the maximum value of input offset voltage allowed for the op-amp.
    2. When an op-amp is selected to meet the requirements for the above, assume that I_{io}=12\mu A. Calculate the maximum value of R_f permitted, assuming that a compensating resistors will be used.

Due to this question being directly related to question 25, I cannot do this question either.