SLEW-RATE DISTORTION
Internally compensated operational amplifiers use a internal compensation capacitor at the
output that is charged and discharged at a rate that is determined by the output voltage swing
and the input frequency. For an applied voltage, the amplified and possibly inverted (for an
inverting amplifier) output will track the input if the rate of change of the output is less than or
equal to the maximum rate of change determined by the maximum current sourced into or
sank from the internal compensation capacitor. For an internal compensation capacitance Cc
and constant maximum charging and discharging currents of ICHARGE and IDISCHARGE the time
required to change the output voltage from an initial voltage of zero to the upper or lower
voltage swing magnitudes is given by t = (Cc ΔVo) / I. For an increase in Vo, ΔVo and ICHARGE
are positive and for a decrease in Vo, ΔVo and IDISCHARGE are negative. Note that for equal
charge and discharge times under the condition where the output is slewing, the charge and
discharge currents must be equal. However, this condition is not true in operational amplifiers
thus the maximum rate or change in the positive and negative directions differ and the
smallest maximum rate of change dictates the maximum rate of change of the input signal.
As an example of slew-rate limitation, the LM348 operational amplifier has the slew-rate
specified as 0.5V/μs which is equal to 5x105 V/s. To determine the maximum frequency that
may be used for a non-inverting amplifier configuration with Gv = 10 V/V and an input signal
of 1 x sin (2πft) :
SR = dvo/dt
vo = 10 x sin (2πft)
dvo/dt = 10 x 2π x f x cos (2πft)
The maximum rate of change of the output is found from dvo/dt = 0 which occurs at t = nπ
where n = 0,1,2, ….
Thus a maximum rate of change is found at the zero crossings of the output sinusoid. It is at
these maximum rate of change points where slew-rate limiting first appears on the output
signal.
To determine maximum applied input signal frequency for a given SR of 0.5V/μs:
SR = dvo/dt
5 x 105 V/s = 20 x π x f so
F = 5 x 105 V/s / (20 x π) V = 7.9577 KHz
Note that for smaller input signal amplitudes that this maximum frequency increases. Thus,
for a small input amplitude, the operational amplifiers use without slew-rate limiting is
increased. Equivalently, for lower voltage gains, the effects of slew-rate limiting are pushed
out further in frequency.
Measurement of the SR:
SR=
SR+ =
V+ – VT1
V+ – V-
If T1 = T2
T1
SR=
+
V+
|V- – V+|
T2
SR- =
2ΔV
ΔT
0
|V- – V+|
T
T1+T2
T2
V-
ΔV = V+ – V-
ΔT = T1 + T2
Page 3
T1
0
T2
Calculation of Gain Bandwidth Products for the Inverting and Non-inverting Amplifiers
ω3dB = ωT / 1 + R2/R1 for both the inverting and non-inverting amplifiers
GBOA = ωT
Inverting Amp:
|Gv|INV-AMP = R2/R1
GBINV-AMP = |Gv|INV-AMP x ω3dB
GBINV-AMP = (R2/R1) x [ωT / (1 + R2/R1)]
GBINV-AMP = R2/R1 x GBOA/ (1+ R2/R1)
To calculate GBINV-AMP from GBOA:
GBINV-AMP = GBOA x [R2 / (R1 + R2)] = GBOA / [(1 + |Gv|-1INV-AMP)]
Observation:
The gain-bandwidth product of the inverting amplifier is the gain-bandwidth product of the
operational amplifier decreased by a factor of 1 plus the reciprocal of the inverting amplifiers
gain.
To calculate GBOA from GBINV-AMP:
GBOA = GBINV-AMP x [1 + (R1/R2)] = GBINV-AMP x (1 + |Gv|-1INV-AMP)
Observation:
The gain-bandwidth product of the operational amplifier is the gain-bandwidth product of the
inverting amplifier increased by 1 plus the reciprocal of the inverting amplifiers gain.
Non-Inverting Amp:
GvNON-INV-AMP = 1 + R2/R1
GBNON-INV-AMP = GvNON-INV-AMP x ω3dB
GBNON-INV-AMP = (1 + R2/R1) x [ωT / (1 + R2/R1)]
GBNON-INV-AMP = (1 + R2/R1) x [GBOA / (1 + R2/R1)]
GBNON-INV-AMP = GBOA = ωT
Observation:
Thus, the gain-bandwidth product of the non-inverting amplifier is equal to the gainbandwidth product of the operation amplifier.