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| Nike computer -
Installed in class room, not BC van.
From Rolf Goerigk
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So - the Nike Analog Computer System
- this is one of four cabinets or racks - includes Zero Set Switches (the brown boxes) each can zero set 12 operational amplifiers. |
| Back of a swing out door/rack. Lots of components - Analog computers of this complexity, 78 Operational Amplifiers, were expensive and heavy. Look at all that hand wiring and soldering. Days of work - Your cell phone likely costs less than many of the components you are looking at - |
| The wall behind a swing out door. Note the many relays to set:
- operational modes, pre-launch, launch, 7 g dive, 1/2 g cruise - and many test conditions, known inputs to get known outputs |
And just for fun, Navy mechanical computing training spotted by Randy Thelen
This information is grouped into the following sections:
- History of the Nike Analog Computer
- Mission of the Nike Computer
- What is an Electronic Analog Computer?
- About the Nike Analog Computer,
- - Digital Computer after 1975
- Solving the Predicted Intercept problem
- Steering Command Details
- Missile Guidance Summary
- About the Nike Plotting Boards
- How does the computer know the radar offsets?
- Gotta have a little fun - Mechanical computers.
- - Digital Computer after 1975
From FM 44-1-2 ADA Reference Handbook, 15 June 1984, see page 21 "Rings of Supersonic Steel"
0) History of the Nike Analog Computer
Now that digital computing logic elements (transistors) are- how many thousands per penny? - and floating point pretty much eliminates scaling,
Digital computing has pretty much taken over from Analog computers for process control.Back in the goode olde dayze,
- beginning before the 1930s and Vannavar Bush's differential analyzer at MIT http://web.mit.edu/klund/www/analyzer/ - until the 1960s
Analog Computing was the practical process control for the masses.- Not many could afford the ENIAC, - or the other massive vacuum tube collections. - And a few hundred tubes are a lot more reliable than thousands. In the late 1930s, mechanical computing elements
- with rather awkward torque amplifiers to handle gain, friction and losses - began to give way to electrical computing elements with vacuum tube amplifiers to handle gain, resistance and losses So - at the beginning of WWII, the needs for solving dynamic fire-control problems
began to be solved by electronic analog computers. http://www.ed-thelen.org/pre_nike.html#gun_dir http://en.wikipedia.org/wiki/Operational_amplifier#1941:_First_.28vacuum_tube.29_op-amp
[Note: most artillery people did not have time to reference the printed fire control tablesgenerated by human computers or by ENIAC.
The tables were needed to generate- cam configurations - potentiometer tapers
for the analog fire control computers. ]
A few generations later (1950), with improvements
(including automatic rather than manual analog amplifier zero setting :-))
the M-33 analog fire control computer for anti aircraft guns was in the fieldand working well - So, by the time the Nike missile system was needed, (1950)
the computing and display elements of the M-33 were used for the related missile guidance problem. Actually, there was practically no choice, digital computing technology would not catch up/supercede analog for many control functions for about 20 another years. In 1974, when most of the Nike systems in the US were being shut down, a digital computer replacement (a militarized DEC PDP-11) was replacing the Nike analog computer in the rest of the world.
1) Mission of the Nike Computer
The Nike Computer had 4 main missions:
- a) Provide Predicted Intercept Point and Predicted Flight Time to Plotting Board - for human viewing
- b) Provide Predicted Intercept azimuth angle to missile during pre-launch
- c) Provide Missile Steering commands after launch
- d) Provide Missile Burst command at correct time after launch
- e) And of course be highly reliable, accurate, testable and maintainable.
a) The Predicted Intercept Point is the point where the missile would intercept the aircraft if:
- the aircraft continued in a straight path and at the same speed
- the missile was fired right now
and the Predicted Flight Time is the time from now for that meeting.
Before launch, this information is useful for the human decision making about when to fire a missile.
After launch, this information is continuously updated based upon actual aircraft flight and missile position and flight characteristics.b) The Predicted Intercept Azimuth is the direction from the launcher to the current Predicted Intercept Point. This direction (azimuth) was sent to the gyro in the selected missile before launch, and was used to provide the missile a sense of "down". This missile gyro and the missile control system kept the belly of the missile "down" and provided the computer and missile a common sense of "down" and left/right.
c) During missile flight, the computer sends Steering Commands to the missile (via the missile tracking radar) to guide the missile to the continuously updated Predicted Intercept Point.
d) The Missile Burst Command is generated by the computer since:
- A human is much to slow and variable to send the command. Since the missile is traveling at about 3000 feet per second, a 0.1 second mistake means a missile explosion 300 feet from the intended location (a clear miss).
- Nike missiles did not "see" the intended target, and could not generate their own burst command. (Although they would automatically burst if they did not receive steering commands for 2 seconds.)
The Missile Burst Command is sent via pulse codes through the missile tracking radar. e) And of course be highly reliable, accurate, testable and maintainable.
In the 1950's, digital computers had tens of thousands of vacuum tubes, and because the vacuum tubes had a mean time to failure of only a few thousand hours, the computers had a mean time to failure of only a few hours. 90 percent "up" time was considered outstanding, and required a round the clock staff of real experts. Digital input and output devices were similarly failure prone. (In the 1970s, when reliable transistors and integrated circuits, and cheaper high speed memory became available, some Nike analog computers were replaced by digital computers.)The only alternative that was reliable enough and accurate enough was the electronic analog computer, which could be implemented for the Nike with fewer than 500 vacuum tubes. There were failures, but the technology was maturing, the tubes were run in a different (not ON/OFF) manner, and the uptime exceeded 99% at most sites. (One failure a month was considered really poor.)
These test points are inputs to computing networks, easily accessable 
Some of the built-in test and trouble shooting aids 
(In the late 1970s, the analog computer was replaced by a digital computer, a PDP-11 W (running the RT-11 operating system. Two of the 4 analog computer cabinets became closets and storage space.)
2) What is an Electronic Analog Computer?
The Nike analog computer was single purpose, a fixed program with a few different modes set by relays to simplify and automate testing and different modes of operation.
wikipedia Analog_computer
An interesting Analog Computer Web site - spotted by Hans Kulk
Another Doug Coward's Analog Computer Museum and History CenterSchematics and Operation Manual for the Heathkit EC-1 here
From "The Analog Computer Museum and History Center"
Analog computer - A computer that performs mathematical operations in a PARALLEL manner on CONTINUOUS variables. The components of the computer are interconnected to permit the computer to perform as a model, or in a manner ANALOGOUS to some physical system.
Electronic analog computer - An analog computer with input, output and program operations that are usually expressed in terms of direct current voltages.
Analog computers may seem to be "simple" or "like a toy computer", in fact they are powerful tools that were used during the 1950s and 1960s to design and test systems like ICBMs, supersonic aircraft and spacecraft. But the analog computer can be used to model any physical system that can be described by mathematical formulas, even more mundane ones from modeling the effects of pollution on the fish population in a river to fine tuning the suspension on a new car design. Analog computers will not only test a fixed design but also allows variables to be quickly changed to test "what if' conditions. By scaling time as an independent variable, physical processes that happen quickly can be stretched out, and processes that happen over a long period can be shortened to make the process easier to study. And it is very easy to study variables at any point in the program while it is running to find faults in the program design.
Although the analog machine is correctly termed a computer, it does not perform its computations by numerical calculations as does the calculator or the digital computer. The analog computer performs mathematical operations on CONTINUOUS variables instead of counting with digits. Positive numbers are represented by positive voltages and negative numbers are represented by negative voltages, all scaled to the computer's working range, usually -100 volts to +100 volts (vacuum tube) or -10 volts to +10 volts (transistorized), Thus the analog computer does not subtract 20 inches from 45 inches to obtain 25 inches but, rather, it subtracts 4 volts from 9 volts to obtain 5 volts. This 5 volts the operator reads as 25 inches in accordance with his arbitrarily specified "scale factor' of 1 volt equals (or is ANALOGOUS to) 5 inches.
The analog computer is basically a set of building blocks, each able to perform specific mathematical operations on direct current voltages and capable of being easily interconnected one to another. Some of the basic operations include addition, subtraction, multiplication, division, inversion, and integration. By interconnecting these building blocks, mathematical equations are modeled. BUT an analog computer is a true PARALLEL computer that can solve one or one thousand equations at the same time. In fact, similar analog computers can be easily connected together to increase their computing power. When you think about the result of many equations being solved simultaneously and becoming the input to other equations, and sometimes these solutions are then fed back or looped back into the original equations with all of the variables changing CONTINUOUSLY with time, then you can get a brief glance into the incredible power of these computers. Output is usually a voltmeter, oscilloscope, or plotter.
Many universities today like Massachusetts Institute of Technology, University of Illinois, University of Notre Dame, and Purdue University offer classes or do research using analog. computers, because they realize that the last chapter of the history of analog computers has not being written. It's an ANALOG universe and analog computers are a natural way to study and understand it.
Prepared by:
We do except donations of your unused analog computing equipment, working or not.
- The Analog Computer Museum and History Center
http://dcoward.best.vwh.net/analog/
From the deployment of Nike in 1954 to the mid 1970's, the Nike Computer was an analog computer. That means that distances, times, and other values were not digital bit representing numbers (like 12.3) but were (in this case) voltage values (like 12.3 volts).
The values as stated above were voltages, and simple circuits (using 76 "operational amplifiers" of 2.5 tubes each) could quickly (1 microsecond):
- add or subtract 2 or more variables
- determine rate of change (of distance giving velocity)
- multiply or divide a variable by a constant
- approximate a function to 1 %
but slower motor driven potentiometers were required to: Each amplifier had a nominal gain of 20,000
- multiply or divide a variable by a variable
- store a variable for a long time (minutes or hours) (not needed in anti-aircraft)
- generate a precision non-linear function
- most amplifiers used "semi-precision" zero set switches with gains of 200, giving effective gains of 4 million.
- about 6 amplifiers used "precision" (re-entrant) zero setting, with gains of 3,000.
There were 2 operational amplifiers using a total of 5 tubes on a chassis. The output tube was a dual triode, 1/2 of the tube was the final amplifier for an amplifier. The "plate" (where the electrons landed) of the final amplifier could be swung between -100 volts and +100 volts using the required external load resistor.
Chassis
DetailFurther details on the operational amplifier are in the Technical Manual TM-9-5000-13-Ch03 DC Amplifier Circuitry 265 KBytes
For images of the motor driven potentiometers see Computer (Servo driven potentiometers) and Computer (Details of Time Potentiometer)
The Nike anti-aircraft problem did not require many slow motor driven circuits (about 7) and used about 100 of the simple fast circuits. It also used numerous relays to change between the various modes of operation (test, pre-launch, post-launch). An interesting characteristic of analog computers is that the circuits tend to run in parallel, The relatively slow circuits all working together easily keep up with the anti-aircraft problem in real time.
An analog computer (distances and times were voltages) used analog (voltage) inputs from the Target Tracking and Missile Tracking Radars.
These values (and derived target and missile velocities) were used to calculate the remaining flight time and Predicted Intercept point. The missile was guided to the predicted intercept point by the computer generated steering commands sent through the Missile Tracking Radar.
For vacuum tube enthusiasts, here are schematics of a
- operational amplifier (42 K bytes) - power supply - voltage reference - + 450 volt 1 amp thyratron power supply
used in the Nike Ajax and Hercules (as well as the earlier M-33 gun laying analog computer and radar system).Another web site Analog Computer Museum and History Center by Doug Coward contains Definitions.
The Nike analog computer did not use integrators, but did use filtered differentiators for velocity determination as well as motor driven potentiometers for multiplying by a variable (including time to intercept) as mentioned above.
Another system of amplifiers and motor driven switches performed as "Zero Set Amplifiers" to:
- zero the bias of the operational amplifiers
- increase the effective gain of the associated operational amplifier(s) (to over 1,000,000)
- alarm on excessive inputs caused by operational amplifier failure or computer not settled to a valid "answer".
A number of preset test cases (switch selectable) helped assure that the computer was performing correctly.
Manual knobs input the offset between the missile tracking and target tracking radars. (For further information, you can jump ahead to 6) How does the computer know the radar offsets?
In the late 1970's a digital computer was made available for the Nike. These were sent to "off-shore" locations as all U.S. sites had been de-activated. It is quite possible that this computer was a Norden PDP-11M. This was a licensed version of the DEC (Digital Equipment Corporation) PDP-11 that was housed in a tougher case and made more vibration resistant and in other ways made more suitable for a military environment.
It is known that the file system format on the floppy disks was RT-11M. (I have two floppies reported to be from a Nike site, but cannot figure out the data/program.) It had two 8 inch floppy disk drives, a printer, (and some I/O cards). As as best I can determine, the tracking antenna potentiometers were retained - the analog voltages being converted to digital for digital computing. Maybe the same for the range pot??
Any information about a digital Nike much appreciated.
Here is Rolf Dieter Görigk's preliminary message - more info to follow:
August 2012, Rolf sent the following
In August 2012, wo Enzo Chieregatti < chrnzo @ libero . it > sent the following:
4) Solving the Predicted Intercept problem
To keep flight times down, (and increase the effective range) the missile is aimed ahead of the target at a calculated Predicted Intercept Point. If the aircraft flies a straight line, the missile horizontal flight path will also be straight. (A dog chasing a target runs directly toward the target, involving a longer run if the target runs straight.)
A person can worry that assuming that airplane flying straight might not be a good assumption, but what better can you make? One can wonder about the 10 million year success of dog-like creatures running directly toward the present position of their intended prey. However their prey can change direction and percent speed much faster than an aircraft. Dog chase path succeeds with a slightly different problem.
The computer has built into it average flight times to various ranges and altitudes. Here is a chart of
Ajax Constant Time Circles. This is an
Ajax time of flight chart. This information is compared with the speed and direction of the target until a valid time of flight to predicted intercept point is computed. This information is presented to the battery commander on the About the Nike Plotting Boards to assist him in making the firing decision.
The computer computes the Predicted Intercept Point by:
- Assuming the designated, tracked Plane will continue on its present course.
- Using a Trial Missile Flight Time, the position of the plane at the end of that time is estimated
- Using the same Trial Missile Flight Time, and a trial missile azimuth, the postion of the missile at the end of that time is estimated
- Based upon differences of estimated tracked plane position and missile position,
- the Trial Missile Flight Time is changed,
- the Trial Missile Azimuth is changed- Go back to step 2, do this continuously.
How Predicted Intercept Point is computed.
At longer ranges (flight times) the Predicted Intercept Point can vary greatly due to target aircraft maneuvers. The battery commander must make allowances for many possibilities.
The predicted time to intercept is also continuously updated during the missile flight to update the predicted intercept point to assist in making steering command commands.
Ajax Constant Time Circles
Ajax time of flight chart
How Predicted Intercept Point is computed.
The missile is launched (essentially) straight up, boosted to about mach 1.7 in 3.4 seconds. It then turns its belly toward the calculated Predicted Intercept (allow 1 second). A sustainer rocket starts to increase the speed to mach 3.5. A full dive command (7 g's) is sent to the missile to dive it from vertical toward horizontal to intercept the flight path of the target. When the missile has reached a vertical angle that will be a good flight path to the intercept point, the full dive command is removed and normal steering begins. For a preview of the "good flight path", jump ahead to End of 7 G dive . (Use your browser's "back" function to return here.)
The missile must not fly directly over the Missile Tracking Radar (MTR) because of limitions inherent in that type of antenna mount and the pointing system. To avoid flying directly over the MTR, special circuits are included in the computer to fly the missile in a path skirting around a flight path over the MTR. This situation is normally avoided by placing the launching area toward the expected direction of enemy aircraft - but the battery can be effective in any case.
After the 7 g dive, the computer flies the missile on a 1/2 g flight path to the predicted intercept point. For further details of the 1/2 g flight path, see page 64 of TM9-5000-3 (4.5 MBytes).
The predicted intercept point is constantly being updated by the computer from data from the target tracking radar and the missile tracking radar. Using the missile position from the Missile Tracking Radar, missile velocity and attitude generated in the computer, and the Predicted Intercept Point, the computer generates analog steering commands in gravity units (g's) for the missile. These commands are sent to the Missile Tracking Radar, where the analog commands are converted into radar pulse sequences indicating the command to the missile.
About 0.1 seconds before the missile will be closest to the target, a missile burst command is send by a coded pulse sequence to the missile by the missile tracking radar. This burst command is decoded and the missile warhead exploded. The goal is to explode the missile just before (10 meters) the missile would impact (or be at the closest point with) the aircraft. This way, the expanding blast of fragements goes through the space where the target aircraft would be - giving maximum damage even if a near miss.
6) Steering Command Details
The steering commands are basically to climb/dive and turn left/right a given number of earth gravitational acceleration units (g forces of fighter plane fame). As an example, the computer might command the missile to turn right at a rate of 1.0 g's. The missile would adjust its fins to turn hard enough so that the left/right accelerometer would indicate 1.0 g's right.Actually the missile fins are 45 degrees from horizontal, and the accelerometers are also 45 degrees from horizontal. The last stage of the computer rotates the command so that a 1.0 g right command will be sent as 0.707 g up/right and 0.707 g down/right which will result in 1.0 g turn right. You do remember your high school trig - don't you? Oh yes, you must be a "rocket scientist".
The missile steering commands are sent in analog form to the Missile Tracking Radar electronics where they are converted to radar pulse pairs which are received by the missile. For a description of the commands as they are sent by the Missile Tracking Radar see Missile Tracking Radar.
About 0.1 second before intercept, a burst command is sent to explode the missile and hopefully disable the target.
Return to beginning of Nike Computer
7) About the Nike Plotting Boards
There were 2 plotting boards
- Horizontal Plotting Board, with 2 pens
x,y - scale = +- 200,000 yards
- one pen always plotted the target
- the other pen plotted
- predicted intercept until the missile is launched
- missile position after missile is launched
- Altitude Plotting Board, with 2 pens
z,t - scale 0-100,000 feet, 0-160 seconds
- the left pen plotted the target altitude vs. time to intercept
- the right pen plotted time to intercept vs.
- predicted intercept altitude until the missile is launched
- missile altitude after missile is launched
There were timing marks every 10 seconds. These were quick jogs up and right.
A launch (fire) mark was a quick jog down and left.
The horizontal plotting board had lights to identify which pen was plotting what.
For a photo of the plotting boards, go to Battery Commander's View of the World.
8) How does the computer know the radar offsets?
The Target Tracking Radar (TTR) is considered the center of the world, well at least as far and the computer and IFC people are concerned. All distances are measured from the TTR. Plotting board distances and elevations are relative to the TTR.The computer must know where the Missile Tracking Radar (MTR) is relative to the Target Tracking Radar (TTR), and also the relative location of the Target Ranging Radar (TRR) relative to the Target Tracking Radar (TTR). This permits the computer to subtract out the positional differences, so that all three radars are, for computational purposes, located at the same point is space.
The offsets of the MTR and the TRR are dialed into potentiomenters located on the computer. The coordinates are as North/South, East/West, Up/Down from the Target Tracking Radar. Any errors dialed into these potentiometers will cause errors in flying the missile to the exact position of the target.
The positional differences of the various acquisition radars are not important because they are always within 50 yards of the TTR and errors in range and parallax due to this offset do not affect operation (primarily the locking on to the designated target by the TTR operators). It is important that the acquisition radars and the TTR (and any area supervision radars) have the same "North" reference to within about a degree for more exact target designation. (Which target is it?)
The Tracking Radars have the same North very precisely due to their alignment procedures.
9) Gotta have a little fun - Mechanical computers.
You have been very good students - serious - no sleeping or whispering - taking notes- ready for a quiz? I haven't the heart - time for fun.
Tim Robinson makes analog computers for fun - out of Meccano building "blocks".a differential analyzer a mini-Babbage machine difference engine
Appendix 1: Chopper Stabilized Operational Amplifiers (Op Amps)
It is very convenient to assume that Operational Amplifiers (Op Amps) for analog computers have- infinite gain (with stability) - no input "offset" voltages or currents Fortunately, they can be made very good so that for many problems errors can be held to less than say 0.01 percent per stage
- the "offset" current to the grid of a good triode (or FET) in on the order of nano amps. Unfortunately, efforts need to be made to reduce off-set errors - An operational amplifier is expected to have zero volts output when the input is zero volts. Failure to do this is called "off-set error". Unfortunately, in real amplifiers, a large number of causes will cause off-set errors which must be continuously corrected.
A principle method of correcting off-set error is to use automatic Zero Set equipment which:
- reduces "offset" voltage - increases amplifier gain without decreasing stability You can manually zero set an operational amplifier by:
- removing the amplifier output from the circuit (no feed back) - connecting the input of the amplifier to analog ground (zero volts) - measuring to output voltage - adjusting the amplifier zero set to achieve zero volts on the output
then re-connecting the amplifier to the circuit for proper operationUnfortunately, temperatures, voltages and other conditions soon change, and you must zero set again, and yet again. Fortunately, a good automatic method of zero setting operational amplifiers was discovered - just in time for Nike.
- (leave the operational amplifier connected in the circuit :-)) - measure the voltage at the "summing junction", the input to the Op Amp - amplify this voltage by say 500 (in the Zero Set Amplifier) * if this voltage is excessive, flash a warning lamp - apply this amplified voltage to the Op Amp zero set input
and do the above over and over again.The voltage measurement and correction can be done in the AC world - which makes life easier :-))
- Connect the input grid of the Zero Set Amplifier to ground
- Connect the output capacitor of the Zero Set Amplifier to ground
- The above steps, 1 & 2, provide a zero reference on the output capacitor
- Disconnect the output capacitor of the Zero Set Amplifier from ground
- Disconnect the input grid of the Zero Set Amplifier from ground
- Connect the input grid of the Zero Set Amplifier to the summing junction (Op Amp input grid)
- Connect the output capacitor of the Zero Set Amplifier to the Op Amp zero set capacitor
- The above 4 steps place a corrective charge on the Op Amp zero set capacitor
- Disconnect the output capacitor of the Zero Set Amplifier from the Op Amp zero set capacitor
- Disconnect the input grid of the Zero Set Amplifier to the summing junction (Op Amp input grid)
- Ready to start step one all over again
With careful design, this switch (and system) can be very reliable, well shielded, with low electrical noise.Further details about the Zero Set are in the Technical Manual TM-9-5000-13-Ch04 Automatic Zero Setting Controls 155 KBytes
So - the Nike Analog Computer System
- this is one of four cabinets or racks -
includes Zero Set Switches (the brown boxes)
each can zero set 12 operational amplifiers.
Transistor Style Zero Set Switch - Hercules only? introduced when? - Our Ajax system had "the old style" machanical below. I don't know how these circuits worked - The "3N93" are listed as "Dual Emitter Chopper Transistors" silicon PNP transistors
The brown box is a zero set switch, capable of zeroing 12 operational amplifiers. The chassis underneath is the Zero Set Amplifier, a gain 300 AC amplifier. 
With the cover off, and one "dual line card" (my name) removed so you can see a typical socket. 
This is the component side of one of the six "dual line cards" (my name). Note the 3N93 transistors. 
and the other side - mostly traces. 
This is the component side of a "power supply card?" (my name) 
and the other side - mostly traces. 
I'm not a transistor guy - if they don't have a heated cathode, they just can't possibly work ;-)) However, for you modern folks - who do believe in magic, here is a spec sheet - look for the 3N93. If anyone knows how the above zero setting circuits work - please send me the word.
Old Style (Mechanical) Zero Set Switch ? Ajax only ?
Appendix 2: Precision Gain Setting Resistors
We are familiar with the usual carbon composition and wire wound resistors, with the stated tolerances of 10% to 1%. These are not nearly accurate enough (nor stable enough) for gain setting resistors in a Nike system with a system error budget of say 20 feet in 25 miles between the errors of the two tracking radars and the various gain sensitive operational amplifiers in the computer.
just for the sake of argument, let us allow error budgets of:
- 7 feet to the Missile Tracking Radar subsystem - 7 feet to the Target Tracking Radar(s subsystem) - 7 feet to the computer subsystem
at a range of 25 miles.Friends, those are tight tolerances !! No room for slop anywhere - The gains of the Missile Tracking and Target Tracking radars in X, Y, and Height must be as identical (and correct) as possible.
An Op Amp gain is determined by the RATIO of the (feedback resistor)/(input resistor). [Assuming of course adequate amplifier gain.] If the feedback resistor is 0.1% low, the input resistor must be an identical 0.1% low. This correct and stable RATIO is attained by several paths:
- Careful precision matching during resistor network manufacture. This is done by selecting and trimming precision resistors monitored by a precision resistor bridge.
- Minimal changes in resistance due to temperature changes. This is attained by using wire wound resistors of low temperature coefficient metal - and non-stress packaging.
Packaging each resistor network so that each resistor is the same temperature as every other resistor in the packaged network. This is accomplished by placing the input and feedback resistors of each op amp into a separate aluminum container so that they get warm and cool together. A draft in the computer cabinet should affect all the resistors of an op amp "identically". The RATIO should be maintained.
If you have comments or suggestions, Send e-mail to Ed Thelen
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Updated Aug, 2012