Describe and Analyze:
• Input bias currents
• Input offset current
• Input offset voltage
• Frequency response
• Slew rate limitations
Ideal op-amps have no limitations, but
real ones do:
• Small bias currents flow into (or out of) both
• The two bias currents are not exactly the
• The differential-pair transistors at the input
are not perfectly matched, causing an input
• The bandwidth is not infinite
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
Input Bias Current
Equal resistance in series with both inputs cancels
almost all the VDROP caused by IIB
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
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
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.
In production, it’s cheaper to buy a better op-amp than
to buy a 10-turn pot and pay someone to adjust it
Output Voltage Swing: VO
Once VO hits the voltage rails, it clips
Output Voltage Swing
Clipping also occurs if output current is too high
Above a certain frequency, the op-amp’s gain drops
Gain vs. Frequency
Bode plots show gain vs. frequency characteristics
• 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)
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
• The intersection point is called the “3dB point” since
at that frequency ACL will be down by 3dB.
Example of the bandwidth of a closed-loop gain
• 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)
a slew-rate of 1V / s (not high, but better than a 741)
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.
• 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
• 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.