Download Operational amplifiers

Operational amplifiers
Building blocks of servos
Operational amplifiers (Op-amps)
Op amp with feedback
Want perfect amplifier
• Infinite gain
• Infinite input impedance
– will not load down source
• Zero output impedance
– will drive anything
Have operational amplifiers
• Gain ~ 106
• Input impedance ~ 100 M W
• Output impedance ~ 100 W
Problems
• Gain too high
– slightest input noise causes max output
• Other problems to be discussed later
Solutions
• Use feedback
• Gain depends only on resistance: Rf / Rin
– can control precisely
Rf
Summing
junction
Vin
Rin V
1
Iin
If
inverting
+
Vout
non-inverting
Op amp
V1 = (Vout - Vin) Rin/(Rin+Rf) + Vin
Vout = -A V1
Vout = -Vin (Rf / Rin) / [1 + (1+ Rf / Rin)/A]
Small gain:
Vout = -A Vin Rf / (Rf + Rin) ~ divider
Large gain:
Vout = -Vin (Rf / Rin)
Note: V1 = -Vout / A ~ 0
Differential amplifier
• Op amp output actually depends on voltage difference at two inputs
• Vout = - (Vin1 - Vin2) (Rf / Rin)
• Insensitivity to common voltage at both inputs = CMRR
• Real op amps have problems with unbalanced input impedance
Solution:
• Add input resistor and pot.
• Op amp with built-in resistors = instrumentation amp. Non-ideal op-amp
Rf
Ideal op-amp circuit
Vin1
Rf
Vin2
Vin1
Rin V
1
Rin
+
inverting
+
Vin2
Rin
Vout
Resistors to compensate
for non-ideal op-amp
~ Rf
non-inverting
Vout
Integrators
• Put capacitor in op amp feedback path
• Vout = - Vin (Zf / Rin) = - Vin / (2 p j f C Rin)
• Similar to low pass filter in high frequency limit
– except applies to low frequencies also
– can show large gain near dc
• Recall V1 ~ 0 forces Iin = -Ifeedback
– charge on capacitor is integral of If
– since Vout = Q/Cf, Vout is integral of Iin
• Result is integrator
Gain response
– integration speed ~ 1 / RinCf
Integrator
log(Vout/Vin)
Cf
If
Vin
Rin V
1
Iin
Single-pole rolloff
6 dB/octave
= 10 dB/decade RC
>60dB
Unity gain at
f = 1 / 2 p RC
0
+
log( f )
Phase response
Vout
Phase
shift
0 degrees
-90 degrees
log( f )
Shunted integrator
• Limit dc gain
• Advantages:
– dc input voltage no longer saturates op amp output
– prevents servo runaway
• Dis-advantages
– long term errors not well corrected by servo
Gain response
Shunted integrator
Max gain = Rf/Rin
at f < 1 / 2 p RfCf
Rf
log(Vout/Vin)
Unity gain at
f = 1 / 2 p RinCf
Cf
If
Vin
Rin V
1
Iin
0
+
log( f )
Phase response
Vout
Phase
shift
log( f )
0 degrees
-90 degrees
Real op amp
Op amp without feedback
• Acts like shunted integrator
Stability condition:
• unity gain freq. before second pole
• otherwise feedback becomes positive
– oscillation
Gain response
Max gain
log(Vout/Vin)
Single pole
6 dB
Unity gain
0
log( f )
Double pole
12 dB
Real op amp
Vin
+
Vout
Phase response
Phase
shift
log( f )
0 degrees
-90 degrees
-180 degrees
Integrator with lead
High frequency gain has minimum value
Purpose:
• Provides phase lead
• Can compensate for pole in servo
Alternate circuits for lead
• Capacitor at input, inductor in feedback
• Overall positive phase
Gain response
– analog to faster than light propagation
– output anticipates input
Single pole
6 dB
log(Vout/Vin)
Min gain
Integrator with lead
Cf
Rf
0
log( f )
If
Vin
Rin V
1
Iin
+
Phase response
Vout
Phase
shift
0 degrees
-90 degrees
log( f )
Summing amplifier
Op amp
• High gain forces V1 ~ 0
• Feedback current must cancel input current
• Generalize to multiple inputs
– Vout = -Rfeedback S Iin = -(Rf / Rin) SVin
– Works because V1 ~ 0
Rf
Vin
If
Rin
Iin V1
• Summing amplifier
inverting
-
Vout
+
non-inverting
– Op amp input is summing junction
– Useful for combining multiple inputs
Summing amplifier
Vin1
Rin1
Vin2
Rin2
Vin3
Rin3
Rf
Summing
junction
If
Iin V1
+
Vout
Drift-compensated integrator
Real op amps have leakage current
• Can saturate integrator
• Compensate with dc current to summing junction
Drift-compensated integrator
Cf
Vin
Rin
If
V1
+V
Integrator
leakage
compensation
-V
Iin
-
Rc
+
Ic
Vout
Trans-impedance amplifiers
• Input is current source
– model as voltage source with high impedance
– Iin = Vsource / Zsource
– Vout = -Zfeedback Vsource/ Zsource = -Iin Zfeedback
Trans-impedance amplifier
• Trans-impedance amplifier
Rf
– current in, voltage out
– gain expressed in Ohms
If
Current
source
Vsource
Zsource
Iin
Iin V1
inverting
+
V1
Vout
non-inverting
Photodiode amplifier
• Photodiode like current source but with capacitor
• Input capacitor causes op amp gain to diverge at high freq.
– Amplifies high freq noise
– Oscillation
Photo-diode amplifier
• Solution:
– Shunt capacitor in feedback
Cs
Shunt
capacitor
Rf
light
Gain response
log(Vout/Iin)
Unshunted
If
Vbias
Ipd
Shunted
+
log( f )
Rpd
Ipd
Cpd
Photo-diode
equiv. circuit
Vout
Integrator design tips
Shunting switch with small value resistor
• Discharges capacitor
– initialize integrator/ servo
– simplify servo testing allow rest of circuit
Resistors on power supply rails
• Limits current to saturated op amp
– prevents burn out
Shunt switch on integrator
Capacitors on supply rails
• Reduces noise
Note on capacitors
• High values
Rs
switch
Cf
– electrolytic, polar
– leakage resistance
Filtered and limited
supply rails
+15V
If
• Use low value in parallel
Vin
Rin V
1
Iin
+
Vout
-15V