ELECTRONIC COMMUNICATIONS SYSTEMS PART 2-1 Fall 2001 ENZO PATERNO

SIGNAL GENERATION Fall 2001 ENZO PATERNO

SIGNAL GENERATION OSCILLATORS PHASE-LOCKED LOOPS FREQUENCY SYNTHESIZERS Fall 2001 ENZO PATERNO

OSCILLATORS THUS ……. OSCILLATORS FEEDBACK OSCILLATORS MANY ELECTRONIC COMMUNICATIONS SYSTEMS (MODULATORS) REQUIRE CONTINUOUS PERIODIC WAVEFORMS (SINUSOIDAL AND NONSINUSOIDAL) THUS ……. OSCILLATORS FEEDBACK OSCILLATORS FUNCTION GENERATORS VCO Fall 2001 ENZO PATERNO

THUS ……. FREQUENCY SYNTHESIS PHASE-LOCKED LOOPS LSI PRESCALERS MANY ELECTRONIC COMMUNICATIONS SYSTEMS REQUIRE A NUMBER ( > 1 ) OF THESE PERIODIC WAVEFORMS AT DIFFERENT FREQUENCIES RELATED TO EACH OTHER (SCALAR MULTIPLES ) THUS ……. FREQUENCY SYNTHESIS PHASE-LOCKED LOOPS LSI PRESCALERS Fall 2001 ENZO PATERNO

THUS ……. PHASE-LOCKED LOOPS FREQUENCY SYNCHRONIZATION MANY ELECTRONIC COMMUNICATIONS SYSTEMS REQUIRE A NUMBER OF PERIODIC WAVEFORMS OF VARIOUS FREQUENCIES THAT MUST BE SYNCHRONIZED TO EACH OTHER. THUS ……. FREQUENCY SYNCHRONIZATION PHASE-LOCKED LOOPS Fall 2001 ENZO PATERNO

OSCILLATORS Fall 2001 ENZO PATERNO

OSCILLATORS OSCILLATE: TO VIBRATE, TO FLUCTUATE BETWEEN ONE STATE TO ANOTHER OSCILLATOR: IS A DEVICE THAT PRODUCES OSCILLATIONS (i.e. GENERATES A REPETITIVE WAVEFORM) FREE-RUNNING OSCILLATOR: IS A SELF_SUSTAINING OSCILLATOR (OUTPUT WAVEFORM IS CONTINUOUS & REPETITIVE). NO EXTERNAL INPUT REQUIRED TRIGGERED/ONE-SHOT OSCILLATOR: REQUIRES AN EXTERNAL INPUT SIGNAL (TRIGGER). BURSTY OUTPUT Fall 2001 ENZO PATERNO

FEEDBACK OSCILLATORS A FEEDBACK OSCILLATOR IS AN AMPLIFIER WITH A FEEDBACK LOOP A FREE-RUNNING OSCILLATOR IS AN EXAMPLE OF A FEEDBACK OSCILLATOR WITH POSITIVE FEEDBACK (REGENERATIVE FEEDBACK) Fall 2001 ENZO PATERNO

FEEDBACK OSCILLATORS UNTUNED OSCILLATOR WIEN-BRIDGE OSCILLATOR HARTLEY OSCILLATOR COLPITTS OSCILLATOR CLAPP OSCILLATOR CRYSTAL OSCILLATOR FUNCTION GENERATOR VCO Fall 2001 ENZO PATERNO

APPLICATION CRITERIA DESIRED FREQUENCY OF OPERATION REQUIRED FREQUENCY STABILITY VARIABLE OR FIXED FREQUENCY DISTORTION REQUIREMENTS DESIRED OUTPUT POWER PHYSICAL SIZE DIGITAL OR ANALOG APPLICATIONS RELIABILITY & DURABILITY DESIRED ACCURACY Fall 2001 ENZO PATERNO

FEEDBACK CIRCUIT MODEL AMPLIFIER + R(S) E(S) C(S) G(S) INPUT OUTPUT FEEDBACK B(S) H(S) WHEN THE ANALYSIS OF FEEDBACK SYSTEMS IS DONE IN THE FREQUENCY DOMAIN, (RATHER THAN THE TIME DOMAIN), WE CALL THIS ANALYSIS APPROACH THE TRANSFER FUNCTION APPROACH. IT INVOLVES LAPLACE TRANSFORMS WHERE: TRANSFER FUNCTION Fall 2001 ENZO PATERNO

FEEDBACK CIRCUIT MODEL AMPLIFIER + R(S) E(S) C(S) G(S) INPUT OUTPUT FEEDBACK B(S) H(S) G(S): FORWARD TRANSFER FUNCTION H(S): FEEDBACK TRANSFER RATIO R(S): INPUT SIGNAL C(S): OUTPUT SIGNAL CLOSED_LOOP TRANSFER FUNCTION Fall 2001 ENZO PATERNO

FEEDBACK ANALYSIS WITH: WITH: USING: BECOMES: AND: ENZO PATERNO Fall 2001 ENZO PATERNO

FEEDBACK ANALYSIS CLOSED-LOOP TRANSFER FUNCTION Fall 2001 ENZO PATERNO

OP-AMP FEEDBACK CIRCUIT Aol AMPLIFIER + Vin Vout FEEDBACK B Aol: OPEN LOOP GAIN, Vout: OUTPUT (NO FEEDBACK) B: FEEDBACK RATIO, Vin: INPUT CLOSED LOOP GAIN Fall 2001 ENZO PATERNO

OP-AMP FEEDBACK CIRCUIT Vin Vout BAol > 0, Acl , NEGATIVE FEEDBACK (DEGENERATIVE ACTION) BAol < 0, | BAol | < 1, Acl , POSITIVE FEEDBACK (REGENERATIVE ACTION) BAol = 1, , OSCILLATION WHEN THE CIRCUIT OSCILLATES, Vin CAN THEN BE REMOVED. Fall 2001 ENZO PATERNO

FEEDBACK OSCILLATORS REQUIREMENTS AMPLIFICATION ONE OR MORE ACTIVE DEVICES CAPABLE OF VOLTAGE AMPLIFICATION (GAIN) POSITIVE FEEDBACK MUST HAVE THE CORRECT PHASE AND AMPLITUDE SO TO MAINTAIN A CONTINUOUS SUSTAINED OSCILLATION (PREVENT CEASING OF OSCILLATION OR AMPLIFIER SATURATION) FREQUENCY CONTROL NEED TO BE ABLE CONTROL FREQUENCY OF OPERATION POWER SOURCE POWER SUPPLY TO POWER CIRCUIT Fall 2001 ENZO PATERNO

FREE RUNNING OSCILLATOR FEEDBACK NETWORK B(f) FEEDBACK LOOP A(f) AMPLIFIER Vin’(t) Vout(t) POWER SOURCE CONTINUOUS OSCILLATIONS A(f): AMPLIFICATION B(f): FEEDBACK FUNCTION OF FREQUENCY. A(f), B(f) ALTER THE MAGNITUDE AND PHASE OF THE SIGNAL NO INPUT SIGNAL - ONLY OUTPUT FEEDBACK Fall 2001 ENZO PATERNO

FEEDBACK ANALYSIS ORIGINALLY, WITH INITIAL SIGNAL Vin’(t) (AT POWER UP) PRODUCES A NEW Vin’’(t) ( ECHOED INPUT SIGNAL) AFTER n TRIPS AROUND THE LOOP, THE NEW ECHO: Fall 2001 ENZO PATERNO

FEEDBACK ANALYSIS NET LOOP GAIN THE ECHO FADES AWAY IF NEGATIVE FEEDBACK IF THE ECHO GROWS WITH TIME POSITIVE FEEDBACK IF THE ECHO REMAINS CONSTANT OSCILLATION Fall 2001 ENZO PATERNO

BARKHAUSEN CRITERION FOR A FEEDBACK CIRCUIT TO SUSTAIN OSCILLATIONS, THE NET VOLTAGE GAIN AROUND THE FEEDBACK LOOP (LOOP GAIN) MUST BE UNITY THE NET PHASE SHIFT AROUND THE LOOP IS A POSITIVE INTEGER MULTIPLE OF 360 degrees (i.e. Vout(t) & Vin(t) ARE IN PHASE = ZERO DEGREES) Fall 2001 ENZO PATERNO

INITIAL CONDITIONS THE FEEDBACK PROCESS HAS TO BE STARTED BY AN INITIAL SMALL FLUCTUATION OF THE CORRECT FREQUENCY FORTUNATELY, ANY SMALL BRIEF FLUCTUATION WHICH CONTAINS SOME POWER AT FREQUENCY, f, WILL START A SEQUENCE OF STEADY OR GROWING OSCILLATIONS SWITCHING THE OSCILLATOR AMPLIFIER ON IS ENOUGH TO INITIATE THE FEEDBACK PROCESS. AS WELL, THE INTERNAL UNCORRELATED NOISE IS ENOUGH TO INITIATE THE PROCESS (NO EXTERNAL SIGNAL REQUIRED TO INITIATE THE OSCILLATION) Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Aol R C R1 Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Vout R R2 C Vin Aol Vout R C R1 NON-INVERTING AMPLIFIER Fall 2001 ENZO PATERNO

NON-INVERTING AMPLIFIER VOLTAGE DIVIDER (FEEDBACK RATIO) SINCE 1 Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Vout = Acl Vin R Zs R2 C Vin Acl A R C Zp R1 Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR MULTIPLY NUMERATOR & DENOMINATOR BY: Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR MULTIPLY NUMERATOR & DENOMINATOR BY: Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR WE KNOW THAT: B BARKHAUSEN CRITERION REQUIRES: ZERO PHASE SHIFT UNITY GAIN Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR ZERO PHASE SHIFT CRITERIA: FOR A ZERO PHASE, Im PART IS ZERO THUS; PHASE = 0, WHEN: Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR PHASE = 0, WHEN: Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR UNITY GAIN CRITERIA (WHILE PHASE = 0): B THUS; AND; Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Aol Acl = 3 R C R1 WE WANT Acl = 3, THUS R2/R1 = 2 Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR TO GUARANTEE THAT THE AMPLIFER WILL NEVER GET INTO SATURATION (DUE TO OVER REGENERATION) AND TO GUARANTEE THAT THE AMPLIFIER WILL NOT CEASE TO OSCILLATE (DUE TO OVER DEGENERATION = STARVATION), WE DESIRE FOR R1 TO BE VARIABLE. AUTOMATIC GAIN CONTROL Fall 2001 ENZO PATERNO

WIEN-BRIDGE OSCILLATOR Aol Acl = 3 R C R1 R1 Rectifier FET IS USED IN ITS VOLTAGE CONTROLLED RESISTANCE REGION Fall 2001 ENZO PATERNO

EXAMPLE FOR THE WIEN OSCILLATOR: FIND AT fo, R = Xc, THUS Zs IS: Fall 2001 ENZO PATERNO

EXAMPLE FOR THE WIEN OSCILLATOR: AT fo, R = Xc, THUS Zp IS: Fall 2001 ENZO PATERNO

EXAMPLE FOR THE WIEN OSCILLATOR: AT fo, R = Xc, THUS B IS: + Fall 2001 ENZO PATERNO

EXAMPLE FIND THE PHASE ANGLE FOR A FREQUENCY ONE OCTAVE ABOVE fo: Fall 2001 ENZO PATERNO

EXAMPLE FIND THE PHASE ANGLE FOR A FREQUENCY ONE OCTAVE ABOVE fo: Fall 2001 ENZO PATERNO

EXAMPLE FIND THE PHASE ANGLE FOR A FREQUENCY ONE OCTAVE ABOVE fo: Fall 2001 ENZO PATERNO

TUNED OSCILLATORS TUNED OSCILLATORS ARE OSCILLATOR CIRCUITS THAT UTILIZE LC TANK CIRCUITS THE FREQUENCY OF OPERATION OF AN LC TANK CIRCUIT IS THE RESONANT FREQUENCY OF THE PARALLEL LC NETWORK Fall 2001 ENZO PATERNO

HARTLEY OSCILLATOR L C THE FREQUENCY OF OSCILLATION IS: ENZO PATERNO Fall 2001 ENZO PATERNO

COLPITTS OSCILLATOR THE FREQUENCY OF OSCILLATION IS: ENZO PATERNO Ca L Cb THE FREQUENCY OF OSCILLATION IS: Fall 2001 ENZO PATERNO

FREQUENCY STABILITY FREQUENCY STABILITY IS THE ABILITY OF AN OSCILLATOR TO REMAIN AT A FIXED FREQUENCY SHORT TERM STABILITY IS A FUNCTION OF FLUCTUATIONS OF DC OPERATING VOLTAGES IN THE OSCILLATOR CIRCUIT MAKEUP LONG TERM STABILITY IS A FUNCTION OF COMPONENT AGING (“LIFE_SPAN”) STABILITY IS POOR FOR THE RC PHASE SHIFT OSCILLATOR (WIEN) AND THE LC TANK CIRCUIT OSCILLATORS (HARTLEY, COLPITTS) Fall 2001 ENZO PATERNO

FREQUENCY STABILITY FREQUENCY STABILITY IS GIVEN AS A PERCENTAGE OF CHANGE IN FREQUENCY (TOLERANCE) EXAMPLE: COMMERCIAL FM BROADCAST STATIONS: CARRIER FREQUENCIES MUST BE WITHIN (88 MHz - 108 MHz) COMMERCIAL AM BROADCAST STATIONS: CARRIER FREQUENCIES MUST BE WITHIN (535 kHz - 1605 kHz) Fall 2001 ENZO PATERNO

FREQUENCY STABILITY FREQUENCY STABILITY IS ALSO GIVEN IN TERMS OF PARTS PER MILLION, PPM. THE MOST COMMON STABILITY VALUES ARE 25, 50, 100 PPM. THE 100 PPM STABILITY FACTOR IS THE MOST POPULAR AS IT IS SUFFICIENT TO RUN MICROPROCESSORS. TELECOMMUNICATION SYSTEMS REQUIRE A TIGHTER STABILITY (i.e. 50 PPM, 25 PPM, 15 PPM) THE LOWER THE PPM, THE MORE EXPENSIVE IS THE CLOCK OSCILLATOR. PRECISION OSCILLATOR (5 PPM) Fall 2001 ENZO PATERNO