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Signal Generators - Contents Basic principles of sinusoid oscillators Oscillators using Op amp and RC Bistable Multivibrators Square and triangular wave generators www.electronics.dit.ie Why Signal Generators? Timing clock for computers and control systems Information carriers for communication systems testing and characterizing electronic devices and circuits www.electronics.dit.ie What Signal Generators? Signals are usually periodic. For examples • Sinusoidal signals --- the basic and most widely used signals • Square waves • Triangular waves • pulses www.electronics.dit.ie Principles of Signal Generators There are two approaches to generate signals: • Linear oscillators an amplifier plus a frequency selective positive feedback network • Nonlinear oscillators using multivibrators www.electronics.dit.ie Principles of Sinusoidal Generators x + y + Amplifier A + Frequency selective network B www.electronics.dit.ie Principles of Signal Generators The system is described by the following equation: Y ( s ) = A( s )[ X ( s ) + Y ( s ) B ( s )] therefore www.electronics.dit.ie Y (S ) A( S ) T ( s) = = X ( S ) 1 − A( s ) B( s ) Principles of Signal Generators Y ( s) = T ( s) X ( s) The output is given by It is desired that the system generate sinusoidal signal with frequency ω0 when there is no input X(s)=0. This implies that the transmission function is infinity at ω0 A( jω 0 ) →∞ T ( jω 0 ) = 1 − A( jω 0 ) B( jω 0 ) or 1 − A( jω 0 ) B( jω 0 ) = 0 ⇒ A( jω 0 ) B( jω 0 ) = 1 www.electronics.dit.ie Principles of Signal Generators The condition is called the Barkhausen criterion A( jω 0 ) B( jω 0 ) = 1 A( jω0 ) B ( jω0 ) e j [φ A ( jω0 ) + φ B ( jω0 ) ] = 1 • The phase of the loop gain is zero φ A ( jω 0 ) + φ B ( jω 0 ) = 0 • The magnitude of the loop gain is unity A( jω0 ) B ( jω0 ) = 1 www.electronics.dit.ie Principles of Signal Generators How to get a more pure sinusoidal wave? φ A ( jω 0 ) + φ B ( jω 0 ) = 0 www.electronics.dit.ie A( jω0 ) B ( jω0 ) = 1 Principles of Signal Generators Nonlinear Amplitude Control • initially |AB| should be slightly greater than 1, so that oscillation magnitude will grow when power is turned on; when the magnitude reaches the desired level, the loop gain to be reduced to exactly unity; • in other word, the loop gain should be nonlinearly dependent on the output magnitude. This can be achieved by inserting a nonlinear network into the feedback path; • a popular nonlinear network is limiter circuit; • the nonlinear network will cause some distortion to the waveform. The distortion will be eliminated by frequency selective network in the feedback loop. www.electronics.dit.ie Principles of Signal Generators www.electronics.dit.ie Op Amp - RC Oscillator Circuit www.electronics.dit.ie Op Amp - RC Oscillator Circuit R2 Z p 1 + R2 / R1 L( s ) = A( s ) B ( s ) = 1 + = R1 Z p + Z s 3 + sCR + 1 / sCR L( jω) = 1 + R2 / R1 3 + j (ωCR − 1 / ωCR ) Firstly, the phase should be zero: 1 ω0CR = ω0CR Then , loop gain be 1, therefore: www.electronics.dit.ie 1 ω0 = CR R2 / R1 = 2 Op Amp - RC Oscillator Circuit: Wien-Bridge www.electronics.dit.ie Op Amp - RC Oscillator Circuit The resistance between a and b decreases with the voltage across them. www.electronics.dit.ie Phase Shifter Oscillator The circuit will oscillate at the frequency for which the phase shift of the RC network is 180 degree. Three is the minimum number of RC sections capable of producing 180 degree phase shift for any high frequency. www.electronics.dit.ie Phase Shifter Oscillator www.electronics.dit.ie The Quadrature Oscillator L( s ) = V02 1 =− 2 2 2 Vx sC R ω0 = www.electronics.dit.ie 1 CR Active Filter Tuned Oscillator www.electronics.dit.ie Active Filter Tuned Oscillator www.electronics.dit.ie Bistable Multivibrators A bistable circuit has two stable output states: Positive saturation or negative saturation A physical analogy for the operation of the bistable circuit. www.electronics.dit.ie When vi increases When vi decreases www.electronics.dit.ie Bistable Multivibrators The output will remain either as L+ or L+ when -VTH <Vi<VTH. When the output is L+, a input voltage higher than VTH will force the output to L-; When the output is L-, a input voltage lower than -VTH will force the output to L+; Therefore the state can be changed by pulse signals with amplitude larger than the VTH. www.electronics.dit.ie Bistable Multivibrators Triggering signal Output signal www.electronics.dit.ie Bistable Multivibrators Noninverting Transfer Characteristics www.electronics.dit.ie Square Wave Generator Using Astable Multivibrators A bistable www.electronics.dit.ie Square Wave Generator Using Astable Mutivibrators www.electronics.dit.ie Triangular Wave Generator Using Astable Mutivibrators www.electronics.dit.ie Monostable Multivibrator: Pulse Generator Aim: To generate a pulse with known height and width in response to a trigger signal. Triggering signal Generated pulse www.electronics.dit.ie Monostable Multivibrator: Pulse Generator www.electronics.dit.ie Monostable Multivibrator: Pulse Generator Operation mechanism: β = R1 /( R1 + R2 ) • What are the steady states (select R4>>R1)? Assume VA=L+. Vc=βL+. D1 is conducting. D2 is also conducting and so VB=0.7v. We can R1 and R2 and R3, such that Vc is lower than VB. Hence this can be a stable state. When VA =L-, D2 is cut off and so Vc=βL- . D1 is cut off and C1 will discharge through R3 and therefore VB will decrease toward Vb=L-. When VB <Vc, the op-amp change the state. Therefore the circuit only has one stable state. www.electronics.dit.ie Monostable Multivibrator: Pulse Generator Operation mechanism: β = R1 /( R1 + R2 ) • Suppose VA=L+, and a negative-going step applied at triggering input; • V will follow the drop and D2 will conduct and Vc will be pulled down. If the triggering low edge is low enough Vc can be lower than VB, and this will make VA=L-; • When VA =L-, D2 is cut off and so Vc=bL- . D1 is cut off and C1 will discharge through R3 and therefore VB will decrease toward Vb=L-. When VB <Vc, the op-amp change the state. • The duration when VA stays in L- will depend on the discharging time constant C1R3. www.electronics.dit.ie Monostable Multiviberator: Pulse Generator What is the width of the pulse? • The initial VB is VD1 (0.7v). When VA=L-, the steady state for C1 to discharge via R3 is L-, and therefore VB = L− − ( L− − VD1 )e − t /( C1 R3 ) • The op amp will flip when VB>VC VB (T ) = βL− = L− − ( L− − VD1 )e −T /(C1R3 ) VD1 − L− 1 ≈ C1 R3 ln T = C1 R3 ln 1− β β L− − L− www.electronics.dit.ie www.electronics.dit.ie