Section 4 Nonlinear Circuits
1 ) Voltage Comparators V P < V N : V o = V ol V P > V N : V o = V oh One bit A/D converter, Practical gain : 10 3 10 6 V OH and V OL should be far apart enough Response Time: t PD : The time it takes for the output to accomplish % 50 of its transition in response to a predetermined voltage step at the input Op amps as voltage comparators: If the speed is not critical op amp is an excellent comparator As a comparator op amp is open loop (no control on V N ) and most of the time it is in saturation
LM 301 (op amp) does not have any internal C C, and has higher slew rate. Compensation Is not necessary in open loop applications. In general op amps are intended for negative feedback operation and their dynamics Are not optimized for open-loop response. General purpose IC comparators: Output and GND are externally accessible (LM 319, LM 339) V P < V N : Q o (on) V CC (Logic) = 5 V, V EE (Logic) = 0 V V P > V N : Q o (off)
2 ) Comparator Applications Level Detectors Nonlinear Circuits Monitors a physical variable that can be expressed in terms of voltage V T = ( 1+ (R 2 /R 1 )) V REF V I < V T : Q o (off), LED (off) V I > V T : Q o (on), LED (on) If the input voltage is equal to V CC, we are monitoring the power supply
On Off Control T < T 0 : VP > VN, Q o (off), LM 395 (on), Heater (off) T > T 0 : VN < VP, Q o (on), LM 395 (off), Heater (on)
Window Detectors When the input voltage falls within a specified band, the output voltage is activated Window detectors are used in production line testing to sort out circuits that fail to meet a given tolerance.
Pulse-Width Modulation Applications are in signal transmission and power control V I : V m sin (ωt) V TR : Triangular wave T L, T H : the time spent by v o in the low and high state within a given cycle of TR D(%) = 100. (T H /(T H +T L )) or D (%) = 100. (V I / V m )
2 ) Schmitt Triggers Positive feedback forces the amplifier into saturation Inverting Schmitt Triggers: V TH = ( R 1 / (R 1 + R 2 )). V OH V TL = ( R 1 / (R 1 + R 2 )). V OL Inverting type threshold controller by the output voltage
A VTC with two separate tripping points is said to exhibit hysteresis : ΔV T = ( R 1 / (R 1 +R 2 ) ) (V OH V OL ) Non - Inverting Schmitt Triggers: V TH = ( - R 1 / R 2 ). V OH V TL = ( -R 1 / R 2 ). V OL ΔVT = ( R 2 / R 1 ) (V OH V OL )
Single Supply Schmitt Triggers: V TL = [( R 1 R 3 )/((R 1 R 3 )+R 2 )]. V CC V TH = [ R 1 /((R 1 R 3 )+R 2 )]. V CC R 4 << R 3 +( R 1 R 2 ) R 5 << ( R 3 + R 4 ) R 4 / R 3 = (V TH -V TL ) / V CC R 2 / R 1 = (V CC -V TL ) / V TH
3 ) Precision Rectifiers Half- Wave Rectifier: V o = V I ; V I > 0 and V o = 0 ; V I < 0 Full- Wave Rectifier: V o = V I ; V I > 0 and V o = - V I ; V I < 0 Rectifier Implementation: In diodes, the non-zero Vd (on) may cause intolerable errors In low-level signal rectification. Half- Wave Rectifiers: Case 1: V I > 0 : D (on), V o = V I Case 2: V I < 0 : D (off), V o = 0 Diode op amp combination : Super Diode
Case 1: V I > 0 : D1 (on), D2 (off)= 0, V o = 0 Case 2: V I < 0 : D1 (off), D2 (on)= 0, V o = (- R2 / R1) VI Full- Wave Rectifiers: V 0 = - ( R 5 / R 4 ). V I -( R 5 /R 3 ). V HW V HW = - (R 2 /R 1 ). V I, V I > 0 V HW = 0, V I < 0 V o = A p. V I, V I > 0 V o = - A n. V I, V I <0 A p =A n =A, V o = A V I R 1 =R 2 =R 4 =R, R 3 =R / 2, R 5 =A.R
AC DC Converters: AC signal is full-wave rectified, low-pass filtered and synthesize a DC voltage AC Dc converters are calibrated to give r.m.s. of the AC signal V(t) = V m. Sin (ω. t), V avg = (2/π). V m, V rms = 0.707. V m, V rms = 1.11 V avg Example of an AC DC converter:
5 ) Peak Detectors We need four blocks for implementing a peak detector: Analog Memory to hold the value of the most recent peak (Capacitor, C H ) Unidirectional current switch to further charge the capacitor when a new peak comes along (Diode, D2) A device to force the capacitance voltage to track the input voltage when a new peak comes along (Voltage Follower, OA1) A switch to periodically reinitialize V o to zero (FET discharge switch in parallel with C) OA2 prevents discharge by R and external load D 1 and R prevent OA1 from saturating after A peak has been detected.
Track Mode: D 1 (off), D 2 (on), OA1 (feedback path, D 2 -OA2- R), No current through R so V o =V I (track) OA1 sources current to charge C H over D 2 Hold Mode: After peaking V I decreases so: D 1 (on), D 2 (off), OA1 (Alternative feedback path), R provides current path for D 1
6 ) Sample and Hold Circuits Nonlinear Circuits SHA: The value of the input signal is captured instantaneously THA: After capturing the signal the circuit tracks the signal until the next Capturing happens (More practical to implement) Track Mode: SW closed D 1 (off), D 2 (off), OA1 (feedback path, SW-OA2- R), No current through R so V o =V I (track), OA1 is a voltage follower Hold Mode: SW open D 1, D 2 prevent OA1 from saturation C H retains whatever voltage it had