6.301 Solid-State CircuitsRecitation 22: More on Transimpedance Amplifiers, and Intro to Zener Diode ReferencesProf. Joel L. DawsonBefore we leave the topic of transimpedance amplifiers completely, there is one “biasing mystery”that is worth clearing up. First, let’s review how a transimpedance amplifier is typically used:Recall that the output voltage, v0, is given byv0= −Z(s) ⋅ iNIdeally, the tranimpedance Z(s) is infinite…we work hard in our design to come as close to thatideal as possible. Accepting for the moment that we have achieved a very large transimpedance,what does that imply about iN? Simple: If Z(s) is huge, and v0 is not, iN must be vanishingly small.This winds up being a key observation for figuring out how these “diamond buffer” circuits work.Let’s look now at a typical implementation of a transimpedance amplifier.R1vIv0−+Z(s)R2iN>6.301 Solid-State CircuitsRecitation 22: More on Transimpedance Amplifiers, and Into to Zener Diode ReferencesProf. Joel L. DawsonPage 2Big question: What sets the quiescent values of I1 and I2?The way to answer is to recognize that we have a Gilbert loop formed by the base-emitter junctionsof Q1− Q4. Let’s assume that the PNPs are perfectly matched to each other, and that the NPNs arealso matched to each other. We have:IC 3Isp⋅IC 4IsN=IC1IsN⋅IC 2IspNow, IC 3= IB1, IC 4= IB 2, and IC1= IC 2 because we can assume that we’re using the amplifier in anegative feedback configuration. So at the end of the day,IC12= IB1IB2IC1= IC 2= IB1IB2(And normally, IB1= IB2)−I2Vpv0IB 2IB1I1↓I2Q3+1Q2Q4I1↓MirrorVnQ1iNMirror6.301 Solid-State CircuitsRecitation 22: More on Transimpedance Amplifiers, and Into to Zener Diode ReferencesProf. Joel L. DawsonPage 3A useful technique when using Zener diodes is to employ some form of “self biasing.” That is to say,the bias current through the Zener diode is determined by the Zener voltage itself, rather than by thevoltage supply. We’ll talk about that in a minute, but first let’s see if we can get a handle on the self-biasing concept.CLASS EXERCISE: For the following circuit, ignore D1 at first.(1) Determine IZ and VOUT.(2) Explain why D1 is important.(Workspace)IOUTVOUTD1R+5VVZIZ−+6.301 Solid-State CircuitsRecitation 22: More on Transimpedance Amplifiers, and Into to Zener Diode ReferencesProf. Joel L. DawsonPage 4Self biasing is important because in order for the Zener diode to provide us with a good, solid voltagereference, it is often critically* important that its current IZ be precisely set. If we can help it, wedon’t want that current to be dependent in any way on the power supply voltage, which can change.*By “critically,” we mean that if we want tiny temperature drifts (~1-2 ppm), we have to be thiscareful.Zener DiodesIt turns out that “reverse breakdown” for a diode is not a destructive event. With good engineering,diodes can be made to be useful under reverse bias as voltage references.By choosing the doping profile of the pn junction, the actual breakdown mechanism traces to one oftwo phenomena:IZIZ− IZ−VZVZ−+VZNormal diodebehavior6.301 Solid-State CircuitsRecitation 22: More on Transimpedance Amplifiers, and Into to Zener Diode ReferencesProf. Joel L. DawsonPage 5(1) Zener Breakdown (Quantum Mechanical Tunneling). Associated Zener voltages areVZ< 5V. These diodes have a soft I/V characteristic and a negative temperature coefficient.(2) Avalanche Breakdown. VZ> 7V (more or less), sharp I/V characteristic, and positivetemperature coefficient.Most “Zener” diodes actually rely on avalanche breakdown.Temperature Compensated Zener DiodesThere are known relationships between the Zener voltage and the resulting temperature coefficientof the device. Here are a few examples:Zener VoltageTC5 V≈ 0 mV/°C6 V≈ +2 mV/°C8 V≈ +4 mV/°C10 V≈ +6 mV/°CIf we know these numbers, we can use ordinary diodes, with their –2 mV/°C TC, to build atemperature compensated reference:6.2V5.6V +2mV / °C( )0.6V −2mV / °C( )6.8V0.6V6.2VLeftunconnected!6.301 Solid-State CircuitsRecitation 22: More on Transimpedance Amplifiers, and Into to Zener Diode ReferencesProf. Joel L. DawsonPage 6If you look at the spec sheet for a commercial Zener diode, you’ll see that there is often one biascurrent at which the diode’s Zener voltage is most stable with changes in temperature. When usingZener diodes, then, we often must go to great lengths to keep the bias current where we want it. Thecircuit shown in the class exercise is one method that we use. Notice that it has a negative outputimpedance: As IOUT increases, VOUT also increases.Here’s an example of how to suboptimally Bias a Zener diode:Numbers: IZ= 7.5 mA, VZ= 6.2V ⇒ R = 1.17kΩA 1% change in VCC means that VZ changed byΔVZ=rZrZ+ R⎛⎝⎜⎞⎠⎟ΔVCC=10Ω(1.18k Ω)⋅150mV = 1.25mVTo see that this is huge, compare:ΔVZVZ=1.25mV6.2V= 200 ppm = (40°C)(5 ppm / °C)VZRVCC= 15VIZ=VCC− VZRΔVZΔVCC=rZR + rZrZ is small signalimpedance of theZener