Consider the circuit depicted in Figure P 11.53(a), which is obtained from the circuit o...

Consider the circuit depicted in Figure P 11.53(a), which is obtained from the circuit of Figure P11.50(b) by using and by replacing with a diode that has an exponential current-voltage relationship. Assume that this relationship is of the form

where M is a constant that depends upon the construction of the diode, q is the charge of an electron, k is Boltzmann's constant, and T is absolute temperature. Note that the idealized relationship of eq. (P11.53-1) assumes that there is no possibility of a negative diode current. Usually, there is some small maximum negative value of diode current, but we will neglect this possibility in our analysis.

(a) Assuming that the input impedance of the operational amplifier is infinite and that its output impedance is zero, show that the following relations hold: