6.301 Solid State CircuitsRecitation 8: LM172 AGC AM IF StripProf. Joel L. DawsonThe LM172 AGC AM IF strip gives us a rather rich set of circuit tricks to add to our toolbox. Oneuseful function to be able to realize in analog systems is a variable gain, where the gain is varied byan analog signal. For example, take the following op-amp circuit:In the small-signal view of the world, the MOSFET looks like a variable resistor (if we bias thingsright). So the transfer function becomesVOUTVIN= −RfRIVB( )Because RIis a function of VB.For our class exercise, let’s explore a bipolar-friendly expression of this concept.VOUT−+RfRI⇒VOUT−+RfVBVIN6.301 Solid State CircuitsRecitation 8: LM172 AGC AM IF StripProf. Joel L. DawsonPage 2CLASS EXERCISE: Consider the emitter-coupled pair:Remembering that gm=qICkT, derive the gain of this amplifier as a function of VE.(Workspace)There are other ways to implement this variable gain idea. In lecture yesterday, Prof. Roberge spokeof “current stealing” as a way of varying the gain. We can examine that concept here in a simplercontext:−+−VEV0RLREVIN6.301 Solid State CircuitsRecitation 8: LM172 AGC AM IF StripProf. Joel L. DawsonPage 3When VG= 0, the output current from QAgets split evenly between Q1and Q2….the gain istherefore 12gmARL, as half of the output signal current is “stolen” by Q1. Looking in Gray and Meyer,we can find the function of ICthat actually winds up going through RLasIC 2IC=β21 +β21 + exp −VGVT⎛⎝⎜⎞⎠⎟=α21 + exp −VGVT⎛⎝⎜⎞⎠⎟The gain for this circuit is thusav=α21 + exp −VGVT⎛⎝⎜⎞⎠⎟⎛⎝⎜⎜⎜⎜⎞⎠⎟⎟⎟⎟gmRLCBIGQAIc−+VGV0RLQ2Q1VINBypass to ground!6.301 Solid State CircuitsRecitation 8: LM172 AGC AM IF StripProf. Joel L. DawsonPage 4which for VG>>kTq= VT( )→ av≈ gmRLVG<< −kTq→ av≈ 0The LM172 has yet another approach to solving this problem. Look at Q2 and Q3, and see anemitter follower Q2( )with a dynamic load (impedance looking into the emitter of Q3).Now, again consulting Gray and Meyer,IC 3=αFIE1 + exp −VCONTROLVT⎛⎝⎜⎞⎠⎟ , IC 2=αFIE1 + expVCONTROLVT⎛⎝⎜⎞⎠⎟For an emitter follower with resistance REin the emitter, the voltage gain isav=β+ 1( )RErπ2+β+ 1( )REVOUTQ3( )⇒↓IEVOUTVCONTROLQ3Q2VIN↓6.301 Solid State CircuitsRecitation 8: LM172 AGC AM IF StripProf. Joel L. DawsonPage 5But here, RE=rπ3β+ 1. Assuming all βs are equal,av=rπ3rπ2+ rπ3Recalling that rπis inversely proportional to ICrπ=βVTICWe can qualitatively sketch rπ2and rπ3 as a function of VCONTROL:The corresponding gain graph for this circuit would then look something likeThere’s also an op-amp hidden in this chip. Can you find it?βVTIEVCONTROLrπ3rπ2VCONTROL121avrπ2, rπ36.301 Solid State CircuitsRecitation 8: LM172 AGC AM IF StripProf. Joel L. DawsonPage 6Look at Q11, Q12, and