1. CHAPTER 10
Op-Amp
Limitations

2. OBJECTIVES Describe and Analyze: Input bias currents
Input offset current
Input offset voltage
Frequency response
Slew rate limitations
Troubleshooting

3. Introduction Ideal op-amps have no limitations, but real ones do:
Small bias currents flow into (or out of) both inputs
The two bias currents are not exactly the same
The differential-pair transistors at the input are not perfectly matched, causing an input offset voltage
The bandwidth is not infinite

4. Input Bias Current: IIB
Op-amps made with BJTs have a very small base current that flows into the input pins (for NPNs) or out of the inputs (for PNPs) on the order of nA
Op-amps made with JFET front-ends have bias currents on the order of pA
Input bias current must be considered when there are large resistor values (RS) in series with the inputs: VDROP = RS  IIB
That VDROP looks like an input signal if it occurs on one input but not the other

5. Input Bias Current
Equal resistance in series with both inputs cancels almost all the VDROP caused by IIB

6. Input Offset Current: IIO
Let IIB+ be the bias current for the (+) input and let IIB- be the bias current for the (-) input. Then the input offset current is: IIO = | IIB+ | - | IIB- |
Even if the resistances (RS) in series with the inputs are perfectly matched, there will be a voltage, call it VIS, that will look like an input signal:
VIS = RS  IIO
IIO for a modern bipolar op-amps can be picoAmps
To minimize VIS, use an op-amp with low IIO

7. Input Offset Voltage: VIO
Input offset voltage comes from the slight mismatch between transistors in the differential pair at the front end of an op-amp.
JFET op-amps can have more input offset than bipolar op-amps.
Input offset voltage for bipolar op-amps can be in the range of milliVolts for old clunkers like the 741, to microVolts, even down to nanoVolts for newer ones like the LT1112.

8. Offset Compensation
In production, it’s cheaper to buy a better op-amp than to buy a 10-turn pot and pay someone to adjust it

9. Output Voltage Swing: VO
Once VO hits the voltage rails, it clips

10. Clipping also occurs if output current is too high
Output Voltage Swing
Clipping also occurs if output current is too high

11. Above a certain frequency, the op-amp’s gain drops
Bandwidth
Above a certain frequency, the op-amp’s gain drops

12. Bode Plots: Gain vs. Frequency
Bode plots show gain vs. frequency characteristics

13. Bode Plots The vertical axis (Y-axis) shows gain in dB.
dB of gain is defined to be: dB = 20  Log(f)
The horizontal axis (X-axis) shows the log of frequency.
A decade is a frequency change of 10 to 1. On a Bode plot, the decades are evenly spaced.
The “roll-off” is how fast the gain drops as frequency increases. A typical roll-off is 20dB per decade.
The frequency where the op-amp’s open-loop gain (AOL) falls to 0dB (AV = 1) is called the “unity-gain bandwidth” (UGB) or the “gain-bandwidth product” (GBW)

14. Bandwidth: ACL & AOL
The closed-loop gain (ACL) of an op-amp circuit is typically much less than the open-loop gain (AOL).
On a Bode plot, ACL is a horizontal line.
At some frequency, call it fB, the horizontal ACL line intersects the roll-off of AOL.
The frequency fB is the bandwidth of the closed-loop circuit.
The intersection point is called the “3dB point” since at that frequency ACL will be down by 3dB.

15. Example of the bandwidth of a closed-loop gain

16. Slew-Rate (SR)
The “slew-rate” of an op-amp is the maximum rate of change of VOUT: SR = VOUT / t
To keep bias currents low, the internal currents in an op-amp are limited. Also inside the op-amp is a a few picoFarads of capacitance.
The time it takes to charge or discharge a capacitor depends on the current: t = (C/I) V
So with C and I fixed, the slew rate is also fixed. It’s a parameter on the op-amp’s data sheet in volts per microsecond (V / s)

17. a slew-rate of 1V / s (not high, but better than a 741)

18. Slew-Rate
An op-amp’s slew-rate (SR) limits the range of sinewave signals it will amplify:
fMAX = SR  106 / 2  VP)
where SR is in Volts/s, and VP is the peak amplitude of the sinewave on the output.
The equation says we can use higher frequencies if we keep the amplitude low, or we can have higher amplitudes if we keep the frequency low.

19. Troubleshooting
As always, check to see if DC voltages are within the correct range.
If an op-amp needs to be replaced, use the same part number if possible.
An op-amp with better specs can usually replace a unit with worse specs (almost anything is better than a 741). But be careful: if the new op-amp has a much higher bandwidth than the original, the circuit might oscillate.
If bread-boarding a new circuit, estimate the parameter values you need for the circuit (slew rate, input offset voltage, etc) and compare them to the op-amp’s data sheet.