Circuit that Avoids Large Feedback Resistor
RR is made large - 10 MΩ or greater - for some Z-meter (ZM) designs with transimpedance amplifiers. A ZM must amplify a wide range of currents, often down to the nA or less range. Photodetector signals can also be very small. As RR becomes very large, the Cf shunting it must be made impractically small for the desired damping, and resistor shunt parasitic capacitance can be excessive. To avert this problem, the following circuit can be used instead.
Let the op-amp be a high-gain, single-pole op-amp, G ≈ –1/s x τT. (See Seemingly Simple Circuits: Transresistance Amplifier, Part 1-- Approximating Op-Amps for derivation of G.) The feedback divider transfer function is
and τf = RR x Cf. When the circuit is solved with Rp = R1||R2,
An ideal op-amp (τT = 0 s) Zm reduces to
For Rp = 0 Ω, the transimpedance reduces further to
The R1, R2 divider output resistance need not be made small (Rp << RR) if a fast × 1 buffer amplifier is inserted between its output and RR and Cf. Then for Rp = 0 Ω and with an op-amp having τT,
This circuit is of the same form as without the output divider but with two differences: RR and τT are both effectively increased by 1/Hdiv.
This two-part article has shown that even a two-component circuit can involve significant dynamics derivations. The derivations are sometimes avoided by designers to reduce math angst, but having the equations offers greater insight into not only how a given circuit behaves but how it will behave under a wide variety of conditions. The transimpedance amplifier analysis, now that it has been carried out, sets forth a design template for such a circuit generally, and it also offers a guiding example of how to go about analyzing the dynamics of amplifiers.
Do not be discouraged from using s-domain algebra to solve circuit dynamics because of cubic or higher polynomials. We encountered a cubic in this exercise but did not have to solve it because some realistic simplifying assumptions reduced the degree of the polynomial to the quite workable quadratic we subsequently analyzed. This is typically the case because circuits tend to be modularized in design into stages that are either isolated from each other or have controlled interactions through controlled port impedances. Then template solutions can be applied to the stages, and are most usually limited to quadratic equations in the s-domain.