Amit Kumar Mishra

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Lecture 26

• Amit Kumar Mishra
• ECE, IIT G

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Common-mode Input Resistance
When a pure common-mode signal vic is applied to
amplifier input(vid 0), total resistance
presented to source is .
Ric is common-mode input resistance. Normally,
Ric gtgt Rid. (gt 1GO) For a purely
differential-mode input signal, input resistance
is
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DC Error Sources Input-Offset Voltage (reason?)
With inputs being zero, the amplifier output
rests at some dc voltage level instead of zero.
The equivalent dc input offset voltage is How to
measure? The amplifier is connected as
voltage-follower to give output voltage equal to
offset voltage. ?
To include effect of offset voltage,
Exact magnitude and sign not known Only worst
case scenario lt 10mV
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DC Error Sources Input-Offset Voltage (Example)?
Output voltage is given by Actual sign of VOS
is unknown as only upper bound is given. Note
Offset voltage of most IC op amps can be manually
adjusted by adding a potentiometer as shown.
Problem Find quiescent dc voltage at
output. Given data R1 1.2 kW, R2 99
kO, Assumptions Ideal op amp except for nonzero
offset voltage.
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DC Error Sources Input-Bias and Offset Currents
((possible project))
Bias currents IB1 and IB2 ( base currents in BJTs
or gate currents in MOSFETs or JFETs) are similar
in value with directions depending on internal
amplifier circuit type.
In inverting amplifier shown, IB1 shorted out by
ground connection. Since, inverting input is at
virtual ground, amplifier output is forced to
supply IB2 through R2 .
Sign of offset current is unknown as only upper
bound is given.
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DC Error Sources Input-Bias and Offset Currents
- Errors in Integrator
At t0, reset switch is opened, circuit starts
integrating its own offset voltage and bias
current. Using superposition analysis, Output
becomes ramp with slope determined by VOS and IB2
and saturates at one of the power supplies. (What
happens without the reset switch?)?
At tlt0, reset switch is closed, circuit becomes a
voltage-follower,
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Frequency Response of Op Amps General Case
Op amps Low-pass amplifier with high gain at dc
and a single-pole frequency response. wB
open loop bandwidth of op amp. wT unity gain
frequency or gain bandwidth product (frequency at
which magnitude of gain is unity (Derive this)).
At w gtgtwB, At w wT, Hence, wT is also called
gain-bandwidth product.
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Frequency Response of Op Amps General Case
(Example)?
Frequency values are often expressed in Hz.

• Problem Find transfer function describing
  frequency-dependent amplifier voltage gain.

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Frequency Response of Op Amps Noninverting
Amplifier
For a closed-loop feedback amplifier
For Ao ßgtgt1,
At low frequencies, gain is set by the feedback,
but at high frequencies, it follows the gain of
the amplifier.
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Frequency Response of Op Amps Noninverting
Amplifier (Example)?

• Problem Characterize frequency response of
  noninverting amplifier.
• Given data Ao 105 100 dB, fT 107 Hz, desired
  Av 1000 60 dB
• Assumptions Amplifier is described by
  single-pole transfer function.
• Analysis

Op amp transfer function
Noninverting amplifier transfer function
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Frequency Response of Op Amps Inverting Amplifier
For Aob gtgt1,
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Frequency Response of Op Amps Inverting
Amplifier (Example)?

• Problem Characterize frequency response of
  inverting amplifier.
• Given data Ao 2X105, fT 5X105 Hz, desired Av-
  100 40 dB
• Assumptions Amplifier is described by
  single-pole transfer function.
• Analysis

Op amp transfer function
Inverting amplifier transfer function
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Frequency Response of Cascaded Amplifiers
Bandwidth of the cascade amplifier is the
frequency at which gain is reduced by -3 dB from
its low frequency value.
Assume that stages do not interact,
For identical stages,
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Frequency Response of Cascaded Amplifiers Example

• Problem Calculate gain and bandwidth of a
  2-stage amplifier with
• Approach . Find Av(0), apply
  definition of bandwidth to find fH.
• Analysis

wH is defined by
Bandwidth of cascaded amplifier is lesser than
that of individual stages.
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Large Signal Limitations Slew Rate and
Full-Power Bandwidth

• Slew rate Maximum rate of change of voltage at
  output of op amp. Typical values range from
  0.1V/ms to 10V/ms.
• For given frequency, slew rate limits maximum
  signal amplitude that can be amplified without
  distortion.

For no signal distortion, Full-power bandwidth
(varies with signal amplitude) is highest
frequency at which a full-scale signal can be
developed.
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Review of limitations

• Non-infinite stuffs!
• Finite gain
• Finite i/p R
• Finite o/p R
• Common mode
• CMRR
• CMIR
• DC errors
• Offset voltage
• Bias currents
• Offset currents
• Large signal
• Slew rate
• Full power bandwidth

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Many Thanks