Quiz 1 Review Op Amps Continued

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Quiz 1 ReviewOp Amps (Continued)

• Professor Sawyer
• sawyes_at_rpi.edu

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Review Topics

• Circuit Analysis
• Filters
• Transfer Functions and Phasors
• Transformers and Inductors
• PSpice Instrumentation and Components

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Circuit Analysis

• Handle combinations of parallel and/or series
  resistors
• Give resistance expressions in equation form,
  rather than as a number.
• Find voltages or currents through any resistor
• Find the total resistance or current
• Know the voltage divider equation
• Find the voltage across a resistor in a voltage
  divider configuration.

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Crib Sheet Highlighter
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Crib Sheet Highlighter
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Circuit Analysis

• Find the total resistance of the circuit, seen
  from the voltage source
• Write equation first then put in the numbers!
• Given V15V, R12000O, R23000O, R3200O, R4800O

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Circuit Analysis

• Find the voltage across R1
• Find the current through R3
• Given V15V, R12000O, R23000O, R3200O, R4800O

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Circuit Analysis

• Just used the following
• Ohms law
• Series and parallel resistance equation
• Voltage divider equation
• Also need to know
• Current divider
• Understand a simulated output

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Filters

• Understand how capacitors and inductors work at
  very low and high frequencies
• Redraw a given RL, RC or RLC circuit at low
  and/or high frequencies and identify low pass,
  high pass, band pass and band reject filters
• Find resonant frequency of RLC circuits
• Find corner frequency of RC and RL circuits
• Identify whether a signal of a certain frequency
  be passed rejected or something in between by a
  filter

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Crib Sheet Highlighter
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Crib Sheet Highlighter
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Filters

• Let Rs0O Redraw the circuit above for very low
  frequencies
• What is Va and Vb at very low frequencies?

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Filters
2) Va0V, Vb0V
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Filters

• Let Rs0O Redraw the circuit above for very high
  frequencies
• What is Va at very high frequencies?

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Filters
2) Va8V If Va is considered the output, what
type of filter is this?
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Transfer Functions and Phasors

• Apply the voltage divider equation and parallel
  and series combination rules to find transfer
  functions using complex impedance expressions
• Simplify the transfer function to find a function
  which governs behavior at low and high
  frequencies.
• Find an expression (or value) for the magnitude
  and phase of the simplified transfer function at
  the corner or resonant frequency

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Crib Sheet Highlighter
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Crib Sheet Highlighter
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Crib Sheet Highlighter
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Transfer Functions and Phasors

• Find the transfer function for the above circuit.
• Write in terms of Z impedance first

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Transfer Functions and Phasors
1) Transfer function for the above circuit.
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Transfer Functions and Phasors
2) Describe the behavior of the circuit at low
frequencies and determine the magnitude and phase
of this circuit.
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Transfer Functions and Phasors
2) Behavior at low frequencies
As ? ? 0
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Transfer Functions and Phasors
2) Magnitude at low frequencies
As ? goes to 0 the magnitude above 1
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Transfer Functions and Phasors
2) Phase at low frequencies
As ? goes to 0 the phase above 0
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Transfer Functions and Phasors
Vout
3) Describe the behavior of the circuit at high
frequencies and determine the magnitude and phase
of this circuit.
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Transfer Functions and Phasors
3) Behavior at High frequencies
As ? ? 8
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Transfer Functions and Phasors
3) Magnitude at high frequencies
As ? goes to the 8 magnitude above 0
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Transfer Functions and Phasors
4) Phase at high frequencies
As ? goes to 8 the phase above 0
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Transfer Functions and Phasors
Vout
4) What is the expression of corner frequency for
this circuit? (See Crib Sheet for short answer)
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Transfer Functions and Phasors
4) What is the expression of corner frequency for
this circuit?
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Transformers and Inductors

• How to apply transformer equations
• Basic characteristics of transformers
• Calculate unknown inductance given the
  capacitance or visa versa
• Calculate resonant frequency given inductance or
  capacitance or visa versa
• Estimate inductance of a coil given some
  dimensions

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Crib Sheet Highlighter
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Crib Sheet Highlighter
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Transformers and Inductors
1) If the output voltage is 3 times the input
voltage what should the constant a be? What
should you set your output inductance to get the
constant a? L11mH, k1, R13O, R23k O, V1300mV
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Transformers and Inductors
L11mH, k1, R13O, R23k O, V1300mV
1) a3
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Transformers and Inductors
2) What is the input impedance of this
transformer? L11mH, k1, R13O, R23k O,
V1300mV
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Transformers and Inductors
2) L11mH, k1, R13O, R23k O, V1300mV
O
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PSpice Instrumentation and Components

• Know which trace corresponds to which voltage
  point on a simple circuit
• Describe specific steps youd follow to obtain a
  certain output for AC sweep, DC sweep or
  Transient Analysis
• Understand how to set parameters for function
  generator
• Understand how to use the oscilloscope

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Op-Amp Circuits Quick Review

• Op-Amps are most commonly used to ________ a
  signal.
• Inputs to the op-amp are called the _______ and
  _______ inputs.
• Unpredictable high gain that is multiplied by the
  input signal is called ____-____ ____ or ______
  ______.
• Extreme gain causes __________.

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Op-Amp Circuits use Negative Feedback

• A balancing act between gain and negative
  feedback for a stable circuit

How do you design negative feedback in the
circuit?
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Op-Amp Analysis

• We assume we have an ideal op-amp
• infinite input impedance (no current at inputs)
• zero output impedance (no internal voltage
  losses)
• infinite intrinsic gain
• instantaneous time response

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The Inverting Amplifier
Is this the same as intrinsic gain?
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Inverting Amplifier Analysis

• Step 0 Understand the Golden Rules!
• Rule 1 VA VB (feedback network brings the
  input differential to zero)
• Rule 2 IA IB 0 (inputs draw no current)

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Inverting Amplifier Analysis
inverting input (-)
non-inverting input ()
Step 1 Re-draw the circuit Remove the op-amp
from the circuit and draw two circuits (one for
the and one for the input terminals of the op
amp).
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Inverting Amplifier Analysis
Step 2 Write equations for the two circuits
inverting input (-)
non-inverting input ()
inverting input (-)
non-inverting input ()
VA0
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Inverting Amplifier Analysis
Step 3 Simplify using Golden Rules and solve for
Vout/Vin
VAVB0
therefore
Golden Rule!
What is this saying about how you can design your
gain?
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PSpice Inverting Amplifier
Use the uA741 op amp to model your
circuits Cant find it? It is in the EVAL
library Add library Eval
Input amplitude 200mV Rf10k O Rin1k O What
should the simulated output look like?
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The Non-Inverting Amplifier
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Non-inverting Amplifier Analysis
inverting input (-)
non-inverting input ()
Step 1 Re-draw the circuit Remove the op-amp
from the circuit and draw two circuits (one for
the and one for the input terminals of the op
amp).
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Non-inverting Amplifier Analysis
Step 2 Write equations for the two circuits
inverting input (-)
non-inverting input ()
Voltage Divider
VAVin
inverting input (-)
non-inverting input ()
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Non-inverting Amplifier Analysis
Step 3 Simplify using Golden Rules and solve for
Vout/Vin
VAVBVin
therefore
Golden Rule!
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PSpice Non-inverting Amplifier
Using the uA741 op amp Input amplitude
200mV Rf1k O Rin1k O What should the
simulated output look like?
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The Voltage Follower
Unity gain amplifier
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Why is it useful?

• In this voltage divider, we get a different
  output depending upon the load we put on the
  circuit.
• Why?

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• We can use a voltage follower to convert this
  real voltage source into an ideal voltage source.
• The power now comes from the /- 15 volts to the
  op amp and the load will not affect the output.

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Integrators and Differentiators

• General Op-Amp Analysis
• Differentiators
• Integrators
• Comparison

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General Analysis Example(1)

• Assume we have the circuit above, where Zf and
  Zin represent any combination of resistors,
  capacitors and inductors.

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General Analysis Example(2)

• We remove the op amp from the circuit and write
  an equation for each input voltage.
• Note that the current through Zin and Zf is the
  same, because equation 1 is a series circuit.

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General Analysis Example(3)
I

• Since IV/Z, we can write the following
• But VA VB 0, therefore

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General Analysis Conclusion

• For any op amp circuit where the positive input
  is grounded, as pictured above, the equation for
  the behavior is given by

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Ideal Differentiator
Phase shift j??/2 - ? ? Net?-?/2
Amplitude changes by a factor of ??RfCin
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Analysis in time domain
I
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Problem with ideal differentiator
Real
Ideal
Circuits will always have some kind of input
resistance, even if it is just the 50 ohms or
less from the function generator.
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Analysis of real differentiator
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Low Frequencies
High Frequencies
ideal differentiator
inverting amplifier
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Comparison of ideal and non-ideal
Both differentiate in sloped region. Both curves
are idealized, real output is less well
behaved. A real differentiator works at
frequencies below wc1/RinCin
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Ideal Integrator
Phase shift 1/j?-?/2 - ? ? Net??/2
Amplitude changes by a factor of ?1/?RinCf
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Analysis in time domain
I
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Analysis in time domain
I
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Problem with ideal integrator (2)
With DC offset. Saturates immediately. What is
the integration of a constant?
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Problem with ideal integrator (2)
With DC offset. Saturates immediately. What is
the integration of a constant?
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Miller (non-ideal) Integrator

• If we add a resistor to the feedback path, we get
  a device that behaves better, but does not
  integrate at all frequencies.

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Behavior of Miller integrator
Low Frequencies
High Frequencies
inverting amplifier
ideal integrator
The influence of the capacitor dominates at
higher frequencies. Therefore, it acts as an
integrator at higher frequencies, where it also
tends to attenuate (make less) the signal.
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Analysis of Miller integrator
I
Low Frequencies
High Frequencies
ideal integrator
inverting amplifier
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Comparison of ideal and non-ideal
Both integrate in sloped region. Both curves are
idealized, real output is less well behaved. A
real integrator works at frequencies above
wc1/RfCf
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Problem solved with Miller integrator
With DC offset. Still integrates fine.
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Why use a Miller integrator?

• Would the ideal integrator work on a signal with
  no DC offset?
• Is there such a thing as a perfect signal in real
  life?
• noise will always be present
• ideal integrator will integrate the noise
• Therefore, we use the Miller integrator for real
  circuits.
• Miller integrators work as integrators at w wc
  where wc1/RfCf

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Comparison

• The op amp circuit will invert the signal and
  multiply the mathematical amplitude by RC
  (differentiator) or 1/RC (integrator)