Operational Amplifier
(OpAmp) Basics
The opamp is basically a
differential amplifier having a large voltage gain, very high input
impedance and low output impedance. The opamp has a "inverting"
or () input and "noninverting" or (+) input and a single
output. The opamp is usually powered by a dual polarity power supply in
the range of +/ 5 volts to +/ 15 volts. A simple dual polarity power
supply is shown in the figure below which can be assembled with two 9 volt
batteries.
Inverting Amplifier:
The opamp is connected
using two resistors RA and RB such that the input signal is applied in
series with RA and the output is connected back to the inverting input
through RB. The noninverting input is connected to the ground reference or
the center tap of the dual polarity power supply. In operation, as the
input signal moves positive, the output will move negative and visa versa.
The amount of voltage change at the output relative to the input depends
on the ratio of the two resistors RA and RB. As the input moves in one
direction, the output will move in the opposite direction, so that the
voltage at the inverting input remains constant or zero volts in this
case. If RA is 1K and RB is 10K and the input is +1 volt then there will
be 1 mA of current flowing through RA and the output will have to move to
10 volts to supply the same current through RB and keep the voltage at
the inverting input at zero. The voltage gain in this case would be RB/RA
or 10K/1K = 10. Note that since the voltage at the inverting input is
always zero, the input signal will see a input impedance equal to RA, or
1K in this case. For higher input impedances, both resistor values can be
increased.
Noninverting Amplifier:
The noninverting
amplifier is connected so that the input signal goes directly to the
noninverting input (+) and the input resistor RA is grounded. In this
configuration, the input impedance as seen by the signal is much greater
since the input will be following the applied signal and not held constant
by the feedback current. As the signal moves in either direction, the
output will follow in phase to maintain the inverting input at the same
voltage as the input (+). The voltage gain is always more than 1 and can
be worked out from Vgain = (1+ RB/RA).
Voltage Follower:
The voltage follower,
also called a buffer, provides a high input impedance, a low output
impedance, and unity gain. As the input voltage changes, the output and
inverting input will change by an equal amount.
Original scheme edited by Bill
Bowden, http://www.bowdenshobbycircuits.info
2nd Order Opamp Filters
The figures below
illustrate using opamps as active 2nd order filters. Three 2nd order
filters are shown, low pass, high pass, and bandpass. Each of these
filters will attenuate frequencies outside their passband at a rate of
12dB per octave or 1/4 the voltage amplitude for each octave of frequency
increase or decrease outside the passband.
First order low or high
pass cutoff frequency (3dB point) = 1/(2pi*R*C)
2nd order low or high pass cutoff frequency (3dB point) =
1/2pi(R1*R2*C1*C2)^.5
Example for 2Khz cutoff frequency  R1=R2=7.95K, C1=C2=0.1uF
Original scheme edited by Bill
Bowden, http://www.bowdenshobbycircuits.info
Single OpAmp Bandpass
Filter
A bandpass filter passes
a range of frequencies while rejecting frequencies outside the upper and
lower limits of the passband. The range of frequencies to be passed is
called the passband and extends from a point below the center frequency to
a point above the center frequency where the output voltage falls about
70% of the output voltage at the center frequency. These two points are
not equally spaced above and below the center frequency but will look
equally spaced if plotted on a log graph. The percentage change from the
lower point to the center will be the same as from the center to the
upper, but not the absolute amount. This is similar to a musical keyboard
where each key is separated from the next by the same percentage change in
frequency, but not the absolute amount.
The filter bandwidth (BW)
is the difference between the upper and lower passband frequencies. A
formula relating the upper, lower, and center frequencies of the passband
is:
Center Frequency = Square
Root of (Lower Frequency * Upper Frequency)
The quality factor, or Q
of the filter is a measure of the distance between the upper and lower
frequency points and is defined as (Center Frequency / BW) so that as the
passband gets narrower around the same center frequency, the Q factor
becomes higher. The quality factor represents the sharpness of the filter,
or rate that the amplitude falls as the input frequency moves away from
the center frequency during the first octave. As the frequency gets more
than one octave away from center frequency the rollof approaches 6 dB per
octave regardless of Q value. Approximate rolloff rates for different Q
values for a single octave change from center frequency are:
Q = 1 = 6 dB
Q = 5 = 18 dB
Q = 10 = 24 dB
Q = 50 = 40 dB
For a single opamp
bandpass filter with both capacitors the same value, the Q factor must be
greater than the square root of half the gain, so that a gain of 98 would
require a Q factor of 7 or more.
The example below shows a
1700 Hz bandpass filter with a Q of 8 and a gain of 65 at center frequency
(1700 Hz). Resistor values for the filter can be worked out using the
three formulas below. Both capacitor values need to be the same for the
formulas to work and are chosen to be 0.01uF which is a common value
usable at audio frequencies. This same filter is used in the "Whistle
On / Whistle Off" relay toggle circuit.
R1 = Q / (G*C*2*Pi*F) =
8/(65 * .00000001 * 6.28 * 1700) = 1152 or 1.1K
R2 = Q / ((2*Q^2)G)*C*2*Pi*F) = 8/((12865) * .00000001 * 6.28 * 1700) =
1189 or 1.2K
R3 = (2*Q) / (C*2*Pi*F) = 16 / (.00000001 * 6.28 * 1700) = 150K
Original scheme edited by Bill
Bowden, http://www.bowdenshobbycircuits.info
Low Power OpAmp  Audio
Amp (50 milliwatt)
The example below
illustrates using an opamp as an audio amplifier for a simple intercom. A
small 8 ohm
speaker is used as a microphone which is coupled to the opamp input
through a 0.1uF capacitor. The speaker is sensitive to low frequencies and
the small value capacitor serves to attenuate the lower tones and produce
a better overall response. You can experiment with different value
capacitors to improve the response for various speakers. The opamp
voltage gain is determined by the ratio of the feedback resistor to the
series input resistor which is around one thousand in this case (1 Meg /
1K). The noninverting input (pin 3) to the opamp is biased at 50% of the
supply voltage (4.5 volts) by a couple 1K resistors connected across the
supply. Since both inputs will be equal when the opamp is operating
within it's linear range, the voltage at the noninverting input (pin 2)
and the emitter of the buffer transistor (2N3053) will also be 4.5 volts.
The voltage change at the emitter of the transistor will be around +/ 2
volts for a 2 millivolt change at the input (junction of 0.1 cap and 1K
resistor) which produces a current change of about 2/33 = 60 mA through
the 33 ohm emitter resistor and the speaker output. The peak output
speaker power is about I^2 * R or .06 ^2 * 8 = 28 milliwatts. The 100
resistor and 47uF capacitor are used to isolate the opamp from the power
supply and reduce the possibility of oscillation. An additional 22uF cap
is used at the noninverting input to further stabilize operation. These
parts may not be needed in such a low power circuit but it's a good idea
to decouple the power supply to avoid unwanted feedback. The circuit draws
about 1.2 watts from a 9 volt source and is not very efficient but fairly
simple to put together. The circuit was tested using a couple 4 inch
speakers located a few feet apart (to reduce feedback) and a small pocket
transistor radio placed on top of the speaker/microphone as an audio
source.
Original scheme edited by Bill
Bowden, http://www.bowdenshobbycircuits.info
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