Current Events
Please Log In for full access to the web site.
Note that this link will take you to an external site (https://shimmer.mit.edu) to authenticate, and then you will be redirected back to this page.
In this problem, we'll study an interesting circuit shown below (which was developed by MIT Professor Bradford Howland in the 1960's). Note that its output voltage is the voltage labeled v_{\rm out}, though we will make use of a separate measurement v_{\rm amp} in our analysis.
For this analysis, you may assume that the op-amp is ideal and that it has net-negative feedback when R_2 \leq R_1, so that, under those conditions you may safely assume that v_+ \approx v_- and that the outputs are not saturated.
Answer the following questions about this circuit:
-
Find the Thévenin and Norton equivalents of this circuit when viewed from its output port, as a function of the circuit parameters V_{\rm in}, R_1, R_2, and R_3. For full credit, clearly show your work.
-
Assume that we then connect this circuit to a load resistor with resistance R_{\rm L} at its output port. If R_1 = R_2 = R_3, determine the current i_{\rm L} into the load as a function of V_{\rm in}, R_1, and R_{\rm L}. How does this current depend on R_{\rm L}?
- Under the assumption that R_1 = R_2 = R_3, this contraption functions like a much simpler circuit component; what is it?
-
Finally, let's check our assumptions about ideality. Assume that in order to operate properly, the voltage v_{\rm amp} must satisfy |v_{\rm amp}| < V_{\rm s}, where V_{\rm s} is the supply voltage to the op-amp. Still assuming that the circuit is connected to a load resistor as in the previous part, and still assuming R_1 = R_2 = R_3, determine the allowable range of R_{\rm L} that ensures proper operation of the circuit.
Upload your answers as a single PDF file, including both your answer and your
work. Please do not include any identifying information in your submission
so that we can grade the submissions anonymously.
