|DIY Op Amps
(c) Nelson Pass, Pass Labs 11/98
|Carl Sagan observed, "If you want to make an apple pie from scratch, you must
first create the universe." If you want to build an audio circuit, you will make the
decision as to how much you will actually build yourself, and how much you will buy
The line is always drawn somewhere. Will you be melting down some sand to
make your transistors? Probably not, but it is always in the mind of the hobbyist to do as
much as possible. Many of the project articles in AE and elsewhere employ commercially
available integrated circuits, usually operational amplifiers.
Monolithic op amps are the gum drops of linear electronics. The Digikey catalog shows
hundreds of such parts with prices ranging from about fifty cents to over twenty dollars,
depending on performance, package, and manufacturer. Virtually all of these parts would
serve in an audio project calling for an op amp.
It is very cheap and easy to use monolithic op amps. In contrast we would suppose that
constructing our own op amps from scratch using transistors (or even tubes) would be a
daunting task, to be tackled only by seasoned engineers, with no guarantee of
This is not the case at all. Simple high-performance op amps are easy to make out of as
few as six discrete components whose total cost is less than a dollar. It is the purpose
of this article to show how easy it is.
Besides the satisfaction of doing it yourself, are there any other reasons to construct
your own op amps? Yes. First you may want some special characteristic such as very high
voltage, or ultra low noise, or high output current, that might be available commercially
but at very high cost. Apex, for example, offers high voltage and high current op amps,
but you should be prepared to pay as much as $682 for a PA03A which can deal with 75 volt
rails and 30 amp output currents.
For audiophiles with a subjective orientation, there is another reason for building
your own op amps which is revealed when you look at the internal schematics of the
commercially available chips. Most of them are designed to achieve specifications which
are not of great importance to audiophiles, such as ultra high gain, or very low DC drift,
or very low dissipation. Their complex topologies reflect these requirements, so you see
many transistors and gain stages in series. The output stages of these op amps are
operated Class B or AB, so they are not as linear as might be achieved with Class A
We see also that monolithic fabrication techniques do not necessarily deliver the best
semiconductor or resistor for each part of the circuit, and by making our own choices in
device selection and testing we can achieve high linear performance with very simple
circuits. I take it as a presumption that simpler circuitry is better, particularly when
applied to audio applications.
|How Op Amps Work
|First, a little tutorial on how op amps work. Fig.
1 shows an op amp, which has five connections to the outside world. Two of
these are power supply rail pins, +V and -V, which for monolithic op amps usually want to
be attached to supply voltages in the range of about 5 to 15 volts each for commercially
available chips. Specialized products work outside this range, from as low as 1 volt to as
high as 500 volts. There is a presumption here that +V and -V are referenced to a ground
potential, but this is not required by the op amp as such. The op amp only needs positive
voltage on the +V pin relative to the voltage on the -V pin to operate properly.
amp has two input pins, designated the positive and negative inputs (+In and In),
which control the voltage at the output pin. For linear operation we will generally want
the voltages appearing at +In and In to be in the range between the power supply
voltages, and in many applications we will see these pins operated near ground potential,
midway between +V and -V.
The output of the op amp can vary between +V and -V, and is controlled by the voltage
difference between +In and In. If the voltage at +In is positive with respect to
In, then the output of the op amp swings positive, toward the +V rail voltage. If
the voltage at +In is negative compared to the voltage at In, the output swings
negative. It only takes a small difference in voltage between the two inputs to create a
large change in the output voltage. This is known as the gain of the op amp.
Thats about it.
|The Role of Feedback
|Of course theres really quite a bit more, and most of it involves the concept of
feedback. The control pins of the op amp are usually so sensitive that it is nearly
impossible to keep the output voltage in the useful (linear) range between the supply
rails without some method of controlling the system, and this method is feedback. Feedback
works to keep the differential input voltage (the voltage difference between +In and
In) very small, which keep the output in the linear range.
We do this by
communicating between the negative input and the output of the op amp. The easiest example
of this is the simple voltage follower of Fig. 2.
In this circuit, the negative input is connected directly to the output, with the result
being that the output of the op amp matches the signal presented to the positive input.
Following the logic of an op amps control pins, we observe that if the voltage
from a signal source driving the positive input were to go positive, the output of the op
amp would start to go very positive. But the output of the op amp being connected to the
negative input would cause it to go positive also, and it will not want to go more
positive than the positive input, or else the output would head off in the negative
direction. Instead it will come very close to the voltage at the positive input, with just
enough difference to allow the op amps output to track the input.
If we want gain, we simply have to fool the negative input into thinking that the
output is smaller than it actually is, as in Fig. 3,
where the negative input sees the output voltage after a voltage dividing network. The
dividing network reduces the voltage by R2/(R1+R2). As a result, the op amp delivers an
output that is a multiple of the input, where the gain is given by the inverse of the
divider: (R1+R2)/R2. As an example, if R1 is 9 KOhm and R2 is 1 KOhm, then the gain would
be 10, and a 1 volt input at +In would result in a 10 volt output.
Another simple feedback connection allows the negative input to be driven by the signal
source, resulting in an inverted output voltage. Fig.
4 shows such a connection, with the gain given by the formula R1/R2. Again
following the logic of the op amp input pins, a positive signal from the source will drive
the negative input so that the output of the op amp goes very negative, and this feeds
back around through R1, greatly reducing the positive voltage. Because in this case the
positive input has been tied to ground, the op amp works to keep the negative input very
close to ground potential. As a result, this circuit is useful as a mixer, since the
negative input can be driven by multiple sources, each with their own resistor, and they
wont interact, since the negative input is held to ground potential, a "virtual
ground", by the feedback loop of the op amp.
A simple rule of thumb about open loop gain and feedback is that the difference between
the open loop gain and the actual output gain is how much feedback has been applied. If
the open loop gain is 60 dB (X1000) and the actual output gain is 20 dB (X10), then 40 dB
(X100) of feedback has been applied.
Certainly there is more to know about feedback, and the above is intended as enough to
start playing. There are a number of excellent sources on op amps and feedback, but my
favorites come from National Semiconductors Linear Application Notes ( Digikey (800)
344 4539, order # 9245B-ND ), where 30 years ago I learned most of what I know on the
subject. Of particular interest is Bob Widlars 1968 piece "Monolithic
Operational Amplifiers The Universal Linear Component", as the legendary
Widlar is widely regarded as the fountainhead of monolithic op amp design.
|Gain Devices: A Short Tutorial
|Op amps are constructed of gain devices and resistors. The gain devices we will deal
with are three terminal devices that are used to control electron flow in a circuit.
Current flows through two conducting pins, governed by a third control pin. The voltage or
current applied to the control pin is taken relative to one of the other pins. In a Fet or
a Tube, the current flowing through the main connections is a function of the control pin
voltage relative to one of the other pins, and in a Bipolar transistor, it is a function
of the current through the control pin.
In a Fet the control pin is called the Gate. In
a Tube it is called the Grid. In a Bipolar transistor it is called the Base. The control
exerted by each of these control pins operates relative to one of the other pins in the
device. In the Fet the Gate operates relative to the Source pin, controlling the current
between the Source and the other pin, the Drain.
In a Tube, the current flows from Plate to Cathode, and is controlled by the voltage
between the Grid and the Cathode. In a Bipolar transistor, the current flows from
Collector to Emitter, and is controlled by the current between the Base and Emitter.
Fig. 5 shows these three types of
devices, and the voltage and current relationships of their pins. Fig. 5A and 5B show an
"N channel" Fet and an NPN transistor, and you will note that 5D and 5E show a
"P channel" Fet and a PNP transistor. These "P" types are like the
"N" types, but have the current and voltages reversed. The availability of these
"negative" versions of the parts is very convenient, and is an advantage over
tubes, which have only "N" type polarity.
For the purpose of simplifying this discussion, I will now refer to Mosfets, at the end
of which we will make note of the major differences between these types of devices.
As noted, the current flowing through the main pins of the device is a function of the
voltage between the control pin and one of the other pins, and in the case of a Mosfet,
this would be between the Gate and Source pins. As the voltage on the Gate becomes
positive relative to the voltage on the Source, current will begin to flow from the Drain
to the Source. This is how the device amplifies electrical signals. The more positive the
voltage between the Gate and Source, the more current from the Drain to Source.
It is of interest to know at what rate the current will change respecting the Gate-to-
Source voltage. This Fig. is called the transconductance, and tells you how much change in
current to expect for a change in Gate voltage. It is often expressed as mhos (the
opposite of ohm), because it describes an inverse of resistance. An ohm is volts divided
by amps, and a mho is amps divided by volts, so that transconductance is seen as the
change of current for a change of control voltage. A device having one mho
transconductance will increase its current by 1A for each additional volt on the gate.
Most signal Mosfets have transconductance on the order of .1 or so, and power Mosfets over
have figures on the order of 10, so that they conduct 10 amps per control volt.
Most N channel Mosfets will begin to conduct somewhere with a gate to source
voltage around +3 to +4 volts, and so in linear circuits you will usually see this range
of DC voltage between the Gate and Source pins.
Naturally, all this assumes that the Drain of the Mosfet has positive voltage applied
to it relative to the Source, otherwise the current wont flow. In much in the same
way you can adjust the knob on a water faucet, but you wont get flow unless there is
For a P channel Mosfet, the action is the same, but the voltages and current flows are
reversed. The P channel Mosfet will begin conducting when the Gate to Source voltage
reaches around 3 to 4 volts.
The gain devices we will consider have three pins, and there are only three ways
to use them. Fig. 6 shows the three ways
to use an N- channel Mosfet, each referred to by a "common pin" name, which is
that device pin which does not carry signal voltage.
The first use is common Drain operation, also known as follower operation. It has
current gain but no voltage gain. The input signal is presented at the Gate, and the
output comes from the Source as nearly the same as the input voltage, but shifted 4
volts DC or so and with a lot more current capacity. The second is common-Source
operation, in which we have both voltage and current gain. The input is at the Gate, and a
phase inverted output signal appears at the Drain. The load for the transistor is shown as
a resistor here, but can be some other, possibly more complex, load.
The third way to use a Mosfet is with common-Gate operation, which has voltage gain but
no current gain. Input appears at the Source; output appears at the Drain. This connection
is most popularly used to form Cascode operation, in which a common-Gate device shields a
The same principles that govern the use of Mosfets applies to other types of gain
devices, but with the following differences:
In JFets, the Gate to Source voltage has a much lower DC value, usually negative, on
the order of 1 volt or so. Also, JFets generally have lower transconductance than
Mosfets, often on the order of .01 or so.
Tubes require much higher voltages, often greater than 100 volts Plate to Cathode, than
solid state devices, and generally conduct less current. For linear operation of a Triode
like a 12AX7, the Grid to Cathode DC voltage is a few volts negative, and we see a
transconductance on the order of .003, or about 3 milliAmps of current for each control
Bipolar transistors have what you would think of as a very high transconductance Fig.,
but that is not an appropriate way of looking at them because the current through the
device is a function of the current through the control pin. The Base pin voltage relative
to the Emitter pin is a relatively constant Fig. on the order of .7 volts, but the current
from the Collector to Emitter is a multiple of the Base to Emitter current. This Fig.,
ranging from less than 10 to as high as 1000, is known as the current gain, or beta, of
the Bipolar transistor.
OK, so now we know enough about gain devices to be dangerous, but keep in mind that
there are many little details about the characteristics of the various gain devices,
details which are generally spelled out in the data sheets and which are worth studying.
So lets build some op amps.
|Step 1: Constructing a
|The key to an operational amplifier is the two gain devices that form the differential
input. You can build a functional op amp from this alone, although more typically it will
be followed by one or more additional stages.
The first step is to construct an input
stage known as a differential pair: two transistors with their Sources tied together, and
fed current at that connection, as shown in Fig. 7.
In this case, current is fed through a current source attached to a negative supply
voltage. Two inputs are available at the Gates, as are two outputs at the Drains, which
then communicate through loads to the positive supply. For simplicity, the current sources
of Fig. 7 are provided by resistors, although a variety of impedance components could be
employed. Among the alternatives for these impedances are active constant current sources,
where the current will not vary with the voltage. In Fig. 7, I1 is the current
sourced to the differential pair which is then evenly divided up into I2 and I3.
The Drains present equal but inverted outputs, which represent the difference between
the inputs. If both inputs see the same signal, then that signal ideally does not appear
at the outputs. It is a differential amplifier, which means any differences in the input
signals at the gates are amplified, and common signal is rejected. For this reason, it is
extremely useful as the input stage for an amplifier, because you can connect an input
signal to one gate and use the other gate to watch the amplifier output.
This output watching is called feedback. The differential pair is used to compare input
and output, and by amplifying their differences it is used to correct for errors at the
Depending on the choice of devices, voltages, and resistance values, the differential
pair of Fig. 7 will have a certain amount of voltage gain, which in this case is around 20
dB (X10). For some purposes, this might be enough, as in the AE projects "Son of
Zen" and "Bride of Son of Zen" in which a power amplifier and accompanying
preamplifier are simply differential pairs, nothing more.
|Step 2: A Second Gain Stage
|Most of the time, though, we want more open loop voltage gain than provided by just a
differential pair so we can have some left over for feedback correction. Also, it would be
convenient to arrange the circuitry so that the output swings the full voltage of the
supplies, which the differential pair is not useful. A second gain stage becomes a
necessity for this.
Fig. 8 shows the
application of a second gain stage to the circuit of Fig. 7. We have added a P channel
Mosfet operating in common Source mode and driving a resistor R3 connected to the negative
supply. R2 is chosen to give about 3 volts DC to drive the Gate to Source voltage of Q3.
This value must often be adjusted to make I2 and I3 equal and create
lower offset input voltage for the op amp, since not every P channel Mosfet will want
exactly 3 volts of drive.
This is a complete and functional op amp. It has an input CMRR of about 42 dB,
and an open loop gain greater than 50 dB. It will swing 20 volts RMS at its output with
low distortion, with a slew rate around 80 Volts/microSecond.
Resistors Ra, Rb, Rc, and Rd are not part of the op amp itself. They are an
"external" network for input and feedback that make this particular op amp into
a linear differential amplifier. Ra is set equal to Rb, and Rc is equal to Rd, and the
gain of the amplifier is Rc/Ra. Fig. 9
shows the distortion curve of this particular circuit at 1 KHz between .1 and 20 volts
output. Below 1 volt, noise dominates the distortion curve. Measured at 2 Volts output,
the distortion is flat from 20 Hz to 20 KHz. The circuit of 8b is set up for a balanced
input, but is easily converted to single input by connecting either of the inputs to
ground. Of course you can replace these four resistors with some other network that
performs a different task.
We can easily create some other versions of this circuit using other types of gain
devices. Fig. 10 shows this circuit
rendered with Bipolar transistors rather than Mosfets. It has a higher open loop gain, and
yields lower distortion and better CMRR figures than the Mosfet circuit. The distortion
curve for this circuit is given in Fig. 11.
Again this is a functional audio gain block that you can build and use. Note that the
PNP transistor 2N4250, has an emitter resistor to lower the open loop gain a bit and
enhance stability, and that capacitor C1 is employed to frequency stabilize the circuit
when operated closed loop.
With Bipolar transistors there is less need to match devices on the differential pair
as long as the current gain figures are fairly high. In this case, the MPSA18s have
betas of several hundred, as does the 2N4250. The Base to Emitter voltages of these
devices is consistent at .65 Volts or so, whereas Fets and Tubes are found to have much
greater relative differences, and benefit more from matching. You can use Bipolar devices
with less gain, commonly around 100 or so, but the performance will decline slightly.
Fig. 12 shows what you might do to
create a Triode op amp using 12AX7s. I did not build this device, but I believe it
would work adequately for some audio applications, and would offer true DC amplification.
The trick of getting the level shifting to properly bias the parallel output tubes lies in
creating a DC voltage source interposed between the output plate of the differential pair
and the grids of the followers. This can be provided by external DC supplies, such as
batteries. This particular circuit would not offer much open loop gain or spectacular
performance, but it does illustrate the potential for operational amplifiers without P
type gain devices.
|Step 3: Still More Gain
|The second gain stage of Fig. 8 was created by a P channel device operated in common
Source mode, which offers both voltage and current gain. Routinely, this second stage
gives us adequate voltage gain for audio applications, but often not enough current gain
to drive lower impedance loads. We can achieve more current gain by adding another gain
stage operated in common Drain, or follower, mode, which gives us current gain but not
Fig. 13 shows the
addition of voltage followers for the circuits of Figs 8 and 10. The open loop output
impedance of Figs. 8 and 10 are simply the values of the resistors attached to the
negative rail, which is 3 Kohms in Fig. 8 and 6.8 Kohms in Fig. 10. With a closed loop,
these values are reduced by feedback, so that 40 dB of feedback would result in functional
output impedance of these resistors divided by 100.
The addition of a follower to Fig. 8 results in an open loop output impedance equal to
the inverse of the transconductance, resulting in about 20 ohms or so. For the Bipolar
device of Fig. 10, it would be the original 6.8 Kohms divided by the current gain (beta)
of the transistor, also resulting in about 20 ohms or so.
The follower not only gives a lower output impedance, but makes the performance of the
op amp less dependent on the load impedance. If you want to drive a lower impedance load,
particularly a loudspeaker, you will want some current gain, and very often you will want
this third stage.
Keep in mind that these issues heavily depend on the requirements of the circuit and
the type of device. As a practical matter, Mosfets give the best combination of
characteristics for performance from the most simple power circuits at higher currents,
but JFets are superior at low power levels for noise and input impedance. Bipolar signal
devices give very high gain in low impedance circuits, and so they often measure better in
cases where the source impedance is low.
|Step 4: More Performance
|Constant Current Sources
So far we have built these op amps using resistors to set
up the currents (bias) through the gain devices. This is a simple and linear way to do it,
but often we want to bias the gain devices with currents that do not vary with voltage, as
they will with resistors. These are called constant current sources. Constant current
sources operate so as to pass a constant current over a wide range of voltages, and in so
doing, they can improve the environment in which the gain devices work. Fig. 14 shows the Mosfet and Bipolar op
amps of Fig. 13 where the resistors have been replaced by constant current sources.
Fig. 15a shows the details of these
current sources as made with Mosfets. It takes about 3.5 volts to bias up the Gate to
Source pins of a Mosfet, so we create a voltage reference using the Zener diode and
resistor. The resistor runs a small amount of current through the Zener diode, which
creates a constant voltage. We use this voltage, 9.1 volts, to drive the Gate of the
Mosfet. The Gate to Source requirements will eat up 3.5 volts of this, leaving 5.5 volts
across the Source resistor, which causes the Drain of the Mosfet to source current as
determined by 5.5/R. The 221 ohm resistor in series with the Gate prevents parasitic
oscillation in the Mosfet, and is generally essential. This current source works quite
well, and can be easily used at high voltages and high currents. It tends to be noisy at
low level usage, but this can be improved by placing a capacitor across the Zener diode,
which is a major contributor to the random noise.
Fig. 15b shows the current sources
as made with Bipolar devices. In this case, the bipolar transistor forming the current
source is driven by bias voltage created using a pair of diodes. The diodes drive the base
of the transistor with about 1.3 volts, and the Base to Emitter junction drops about half
of that, leaving about .65 volts left over to determine the current through the Emitter
resistor of the current source. The current coming out of the Collector will be relatively
constant at .65/R.
Fig. 15c shows current sources
formed from JFets. JFets normally have a negative gate voltage, and so they conveniently
form a self-biased current source as shown. For an N channel device like the 2SK170, the
gate voltage is about -.3 volts, so we simply set the source resistor value for current
determined by .3/R. As shown, the current sources are set for 4 milliAmps. Besides
simplicity, JFets have the advantage of being very low noise. On the down side, they are
limited in their ability to handle high voltages and dissipate wattage.
The choice of which device to use for current sources is up to you. There is not
requirement that you use Mosfets current sources in the Mosfet op amp, nor is there are
requirements that you must use current sources everywhere in the circuit. You are free to
use current sources where you choose, or not, depending on the results you want.
The willingness to experiment is very important to getting the results you want. You
can evaluate performance subjectively or objectively, but you should always be prepared to
try things out.
Using a constant current source to bias the differential pair (I1) is
probably the most key improvement. It has the advantage that it does not raise the open
loop gain, but dramatically improves the power supply rejection (PSRR), making the
performance independent of supply fluctuation and noise. It also greatly improves the
common mode rejection (CMRR) of the input stage, typically by a factor of 20 to 30 dB.
The second most useful spot for a constant current source is where the second gain
stage is loaded (I4). This raises the gain of this stage, lowers the
distortion, and again improves the power supply rejection.
I have not shown current sourcing where R2 is replaced by a constant current source,
and this is a technique often used in monolithic op amps as it increases the gain of the
differential pair and raises the open loop gain of the op amp, sometimes dramatically.
Sometimes it is necessary when you need very high gain, such as in phono stages, but it is
often more trouble to implement than it is worth in line level applications. The
requirement for low voltage across this current source makes it a little more difficult,
and we will leave it as a future advanced exercise.
Current sourcing the third output follower stage (I5) gives some linearity
improvement and improves the efficiency and PSRR of a single-ended Class A output stage,
but is often not essential to the performance of a line level stage with a regulated
Lowering the Noise
Part of having low noise is either having high power supply rejection (PSRR) or a quiet
power supply. It is not difficult to use quiet current sources or a quiet power supply or
both. After that, the noise will depend heavily on the quality of the input transistors.
We note on the distortion curves of our op amps that the distortion curve is seen to
rise as the output goes below a volt or so. This is mostly due to random noise in the
differential input devices. For the Mosfet circuit of Fig. 8, this amounts to about 10
microVolts of noise. For the Bipolar circuit of Fig. 10 it is about 2 microVolts.
For even lower noise, it is possible to use low noise JFets as the differential pair,
giving random input noise on the order of .4 microVolts. Fig.
16 shows the circuit of Fig. 8 but with 2SK389 dual low noise JFets dropped
in. The distortion and noise at low levels drops by an order of magnitude, but the
performance at higher levels is nearly identical, as seen in Fig.
|All of the example op amps presented here have used 32 Volt rails, which represents a
reasonably good trade off between performance of the simple circuits and the ratings of
the devices. We can get some interesting improvements at higher voltages with higher
voltage devices and use of cascode operation, but that is beyond the scope of what we are
trying to accomplish here.
Projects using monolithic op amps routinely have plus and
minus 15 volt rails, as this represents the supply ratings of many devices. You may find
yourself wanting to transplant some of our example circuits into these projects, in which
case you have the choice of either creating higher voltage supplies or adjusting the
biasing of the op amps.
As you raise the supply rails, the values bias resistors R1, R3, and R4 are increased
to give the same current, and at higher values they look more like constant current
sources to a given level of signal. This is a very easy way to improve the performance
without introducing more parts.
If you choose to use the lower 15 Volt rails of an existing project, you will want to
adjust the resistors which determine I1, I4, and I5. As a
practical matter, you can simply halve their values to get the same amount of current, and
the reduction in performance will be nominal, but not likely a real problem. You will not
be halving the value of R2 as long as I1 remains the same.
None of these bias values are critical; in fact I pulled them out of the air without
any attempt to optimize the performance. If you play around with the various values of
resistance and current, you may find the performance improved. If you have a distortion
analyzer, it is perfectly acceptable to tweak the values for a lower distortion number.
It is highly probable that you will want to adjust the resistors in a particular
application to get low DC offset at the output, so dont be afraid to play around.
Remember, none of these parts costs as much as a dollar.
Likewise, feel free to substitute different kinds of gain devices in and out.
The circuits given here will work with just about any kind of part, and you can compensate
for many differences simply by adjusting R2.
There will be times when your circuits will oscillate, which is one of the best reasons
for owning an oscilloscope. Oscillation, in which the feedback loop chases its own tail,
causes a lot of distortion and noise. There are several things you can do to eliminate or
First, bypass the power supply leads to ground with capacitors near the circuit.
Second, always place some resistance (a couple hundred ohms or so) in series with the
gate of any Mosfet.
Third, never hook the output of a small current op amp to the outside world without
some resistance in series with the output, at least 100 ohms or so.
Fourth, use compensation capacitors in the circuit such as C1 in Fig. 10, and
dont be afraid to adjust their values.
Fifth, place resistance in series with the Source or Emitter pins of gain devices Q1,
Q2, and Q3 to reduce their gain. If you use resistance on Q1 of the differential pair,
then use the same value on Q2 to keep them equal.
|This article has been intended only as a beginning tutorial, something to get you
started playing with and building your own op amps. Going through the literature on op amp
schematics, applications, and characteristics of gain devices, you will see that we have
just scratched the surface. Nevertheless, you can take the circuits presented here and put
them to use directly or extend them in ways limited only by your imagination and
willingness to experiment. Fooling around with this stuff is how you learn.
At our web
you will find copies of other DIY projects which will help by providing more tutorial
discussions and more examples of op amps put to work. You can e-mail me from there, or
more directly: email@example.com
. Sooner or later everyone gets a reply, sometimes the one desired.
I get a lot of mail asking for the names of books that will teach you how to build
amplifiers, and I dont have a good response. As mentioned before, the National
Semiconductor Linear App Notes is a great source of information. Also, "The Art of
Electronics", by Horowitz and Hill, Cambridge University Press, is an excellent book
that I keep around. Both of these sources have more information than you are likely to
|Sidebar: Op Amp Specifications
|There are a number of useful specifications regarding operational amplifiers, whether
they are monolithic chips or do-it-yourself discretes. Here is a quick glossary of the
most commonly quoted specs. Remember that decibels (dB) is a nonlinear scale for
describing the ratio of two numbers, and that every factor of 10 adds 20 dB.
specifications are the results of the laws of nature and the decisions made by the
designer. Typically you have to give up something somewhere to get something else, so it
is always appropriate to consider what specifications are important to you, and what
numbers are appropriate, and what you give up to get them. If one design delivered it all,
then there would only be one design. From the catalogs, I would guess that there are
thousands of designs.
Open Loop Gain: The ratio of output voltage change over differential input
voltage change. If a difference of .001 volt between the positive and negative inputs
results in 1 volt of output, the gain is 1000, or 60 dB. Most op amps are designed for
very high gain, often on the order of 1 million (120 dB), but this is not always necessary
or desirable, as you often trade off complexity and bandwidth, and when you design your
own op amps you can adjust the gain to your needs.
Input Offset Voltage: You can imagine that if the differential inputs of the op
amp were perfectly matched, then the output of the op amp would settle to the midpoint
between the supply rails when the differential input voltage is 0. Typically it does not,
and the slight input voltage required to place the output between the supply rails,
typically measured in milliVolts, is known as the input offset voltage.
Input Impedance: The input pins of an op amp have a finite impedance, and will
draw some small amount of current due to an input voltage. Generally we want input
impedance to be high, so that it doesnt load down or otherwise distort the source,
but there is a category of op amp using "current feedback" in which the input
impedance of the negative input is low. If you need or want high input impedance, JFets
give the best performance, followed by Mosfets and then by Bipolar transistors.
Input Bias Current: If the input pins are attached to bipolar transistors, there
will be a small but measurable DC current flowing through the input connections which
might be important in some applications. JFets and Mosfets do no suffer from this in any
Common Mode Input Rejection Ratio: While only the differential input voltage is
what is supposed to drive the op amps output, we find that the voltage which is
common to both inputs can have an effect too. The amount of this effect is abbreviated as
the CMRR, and is given in decibels. An op amp with a CMRR of 60 dB and an open loop
gain of 60 dB will have 1 Volt of output or each volt of common mode input signal. If 40
dB of feedback is used to reduce the gain to 20 dB, then it will have .01 Volt output for
each volt of input common mode.
Power Supply Rejection Ratio: The ideal op amp does not depend on the value of
the supply voltages, nor does any supply noise appear at the output. As a practical
matter, this will not be the case, and like CMRR, this is expressed as in dB. Monolithic
op amps usually have very high PSRR Fig.s. Home brew op amps typically are not as good,
giving an excuse for having quiet regulated supplies.
Power Supply Range: The functional range of +V and -V. Traditionally, projects
will choose 15 volt supply rails. For line level audio applications, this is often
adequate, however we might want higher voltages for use in power amplifiers, or to achieve
greater linearity from the gain devices used in the op amp, but this will be limited by
the ratings of the gain devices.
Output Impedance: Just as the input pins have a finite impedance, so does the
output pin, only here we want the impedance to be low. Often it is not actually very low,
but is made effectively low by the action of the feedback loop. For example, an op amp
whose intrinsic "open loop" output impedance is 10 ohms and whose open loop gain
is 1 million (120 dB), will operate as a follower with an output impedance of 10
millionths of an ohm. A follower stage at the output of the op amp is routinely use to
deliver a low output impedance, if needed.
Output Current: Output current is limited by the gain and dissipation capacity
of the op amps output stage, and for monolithic devices, this is on the order of 10
milliamps (.01 amp) or so. Audio power amplifiers are usually just big op amps whose
output current ratings are several amps, sometimes hundred of amps.
Bandwidth: The op amps open loop gain will decline , or roll off, with
frequency, and the frequency at which this begins to occur is the bandwidth of the op amp.
Many monolithic op amps with very high gain will experience this roll off below audio
frequencies, such as 10 Hz. This is not necessarily the response of the op amp with a
feedback loop, as the feedback offers correction, however the ability of the feedback to
correct for declining open loop declines at the same rate.
Slew Rate: Closely related to the bandwidth, the question is "How fast can
the output move from one voltage to another?" Monolithic devices have speeds anywhere
from less than 1 volt per microsecond to over 1000 volts per microsecond. Line level audio
circuits experience signal speeds as high as .1 volts per microsecond with music, and the
project circuits here all do around 80 volts per microsecond or more.
Distortion: All circuits distort the signal, and the question is simply how
much. The most common specification is Total Harmonic Distortion plus Noise (THD+N) which
you see in the distortion curves here. When a simple single frequency signal (a sine wave)
is distorted by a circuit, additional components appear at multiples, or harmonics, of the
original frequency. Adding up the energy in these harmonics plus the noise gives a
percentage number. Obviously low distortion and noise is better but such emphasis has been
placed on this single number that many audiophiles are concerned that some other
performance factor has been traded off against this. There is a common belief among
audiophiles that Distortion does not tell the whole story.
|Sidebar: Matching Differential Gain
|The best performance is obtained from differential pairs where the devices are
matched. You can often buy them this way on a single chip, but it is not difficult to do
some simple matching yourself. The test is simple and requires a power supply, a resistor,
and a DC voltmeter.
Fig. 18 shows
the test hookup for N channel Mosfets. The supply source resistance (R1) is nominal, and
is found from I2 = (V - 3)/R1, where V is the supply voltage and I is the
nominal current you intend to run each input device at. In the op amp circuits presented
here, I2 is about 2 milliAmps. Given a 15 Volt supply, R1 should be about 6000
We are looking to match the voltage across the Mosfet, which will be around 3 to 4
Volts. Keep in mind the caveats about electrostatic discharge: touch ground before you
touch the parts.
Fig. 19 shows the matching circuit
for NPN transistors. We use the same R1 value, but the resistor in series with the Base
should be chosen so that a typical part has about 4 Volts across Collector to Emitter. For
transistors with a current gain of 100, the resistor will be about 200 KOhms, allowing
current of about 20 microAmps to flow through the Base and causing 2 milliAmps to flow
through the transistor. For higher gain devices, higher values of base resistance will be
appropriate, chosen to place about 4 Volts or so across the transistor. As before, we
match devices for the same voltage across the device given the same Base resistor.
Fig. 20 shows the matching circuit
for N channel JFets. Because JFets do not require a positive control voltage, they are
conveniently self-biasing in this test. Choose the value of the resistor so that the
typical JFet operates at 2 milliAmps, as determined by the voltage across the resistor and
the value of the resistor, where I = V/R. For example, if the voltage is .3 Volts, then
.002 = .3 / R, which results in an R of 150 Ohms. In this case we measure the voltage
across this resistor, not R1, and we want our matched devices to have the same voltage.