Lecture 15
Filters and Op Amps
Mark Horowitz
Stanford University
horowitz@ee.stanford.edu
Copyright © 2014 by Mark Horowitz
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Roadmap
We start by finishing up the material on RC filters, and show
how on can create low-pass, high-pass, and bandpass filters
using just resistors and capacitors. We also show how it is
easy to understand how these circuits work by using the
concept of impedance.
Next we turn to the problem of measuring the small electrical
signals that the body produces. We introduce a new
component, an Op Amp, that can amplify the small signal, and
show how using feedback we can build an amplifier with the
gain that we need. In the next lecture we will show how to
combine impedance ideas with op amps to create filters that
have a peak gain greater than one.
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Learning Objectives
•  Use impedance to solve a circuit with multiple capacitors
•  Understand what an op amp is:
–  The inputs take no current
–  The output is 106 times larger than the difference in input
•  The “golden rules” of op amps
–  Input current is 0; Vin- = Vin+
•  Be able to use feedback to control the gain of the op amp
–  For inverting and non-inverting amplifiers
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PREVIOUSLY IN E40M
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Impedance
•
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Frequency Domain Analysis
•
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Want to Measure our Heart’s Electrical Signal
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RC FILTERS
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RC Circuits are Sometimes Called Filters
•  Is a circuit that changes the relative strength of different frequencies
•  Named for what they do
–  Low pass filter:
•  Passes low frequencies, attenuates high frequency
–  High pass filter
•  Passes high frequencies, attenuates low frequencies
–  Band pass filter
•  Attenuates high and low frequencies, lets middle frequencies pass
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High Pass Filter
•  Another voltage divider
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High Pass Filter
•
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Low Pass Filter
•
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Bandpass Filter?
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Bandpass Filter
•  Look at the circuit at different frequency regions
–  Low, middle, high
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Bandpass Filter: Find Z1 & Z2
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Bandpass Transfer Function
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What is the Output Waveform?
•  With frequency analysis we generally don’t compute the output
–  We are interest in what the circuit does to the input
–  And the transfer function provide this information
•  If we want the output waveform
–  Simulate the differential equation
–  Multiply the Fourier coefficients with the transfer function
•  Then generate the waveform by adding the sinewaves
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OP AMPS
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Op Amp
•  Is a common building block
–  It is a high-gain amplifier
–  Gain is 10K – 1M
•  Output voltage can be + or –
–  Often runs from +Vdd and -Vdd supply
•  But gain of 10K-1M is too large for our needs
–  And we want to build circuits with well controlled gain
–  Using feedback will accomplish both objectives
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Op Amp Behavior
•
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Since the Output Swing is Limited
•  The high gain only exists for a small range of input voltages
–  If the input difference is too large, the output “saturates”
•  Goes to the max positive or negative value possible
•  Close to supply voltages
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What Does This Do?
Vcc = 5 V
5
+
4
vin +
-
+
-
+ vout
vout
2.5 V
2
1
-
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How To Get A Useful Amplifier
•  The gain of the op amp is to high to make a good amplifier
–  We need to do something to make it useful
•  We will use analog feedback to fix this problem
–  Feedback makes the input the error between the value of the
output, and the value you want the output to have.
•  Let’s see how to do this
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Connect Vout to Vin-
Vcc = 5 V
+
vin +
-
+
-Vcc = -5 V
vout
-
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Op-Amp Characteristics
•
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Ideal Op Amps
The Two Golden Rules for circuits with ideal op-amps*
No voltage difference between
op-amp input terminals
No current into op-amp inputs
* when used in negative feedback amplifiers
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USEFUL OP AMPS CIRCUITS
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Non-inverting Amplifier
At node vn
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Inverting Amplifier
vn = v p = 0
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Summing Amplifier
KCL at the summing point (or summing node):
Output voltage is a scaled sum of the input voltages:
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Current-to-Voltage Converter
KCL at the vn node:
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Learning Objectives
•  Use impedance to solve a circuit with multiple capacitors
•  Understand what an op amp is:
–  The inputs take no current
–  The output is 106 times larger than the difference in input
•  The “golden rules” of op amps
–  Input current is 0; Vin- = Vin+
•  Be able to use feedback to control the gain of the op amp
–  For inverting and non-inverting amplifiers
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Reading
A&L: Chapter 15, pp. 863-866.
•  Noninverting Amp
–  http://www.electronics-tutorials.ws/opamp/opamp_3.html
•  Inverting Amp
–  http://www.electronics-tutorials.ws/opamp/opamp_2.html
•  Summing Amp
–  http://www.electronics-tutorials.ws/opamp/opamp_4.html
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