Analog Multiplier Circuit (4-quadrant): How does it work?

[@STEMprof]

A few related circuit videos: Op Amp Amplifier with Electronic Gain Control kzbin.info/www/bejne/hKCxmISml89qbbs Analog Computer Power Raiser V1^V2 kzbin.info/www/bejne/h5aWlIxvf7itj8k Instrumentation Amplifier with Electronic Gain Control kzbin.info/www/bejne/eWXXmJuQYtZpkNU VCA Electronic Gain Control: Voltage-Controlled Attenuator kzbin.info/www/bejne/mXfdio2phaqnhpI Square Root Analog Computer Circuit kzbin.info/www/bejne/epTXZp-tht53q8U , Analog Voltage Divider kzbin.info/www/bejne/aJLbemiiaMiZbMU , Logarithm Amplifier (Log calculator analog circuit) kzbin.info/www/bejne/r367d62to9CSZ9k , I hope these examples of Electronic Gain, Attenuation Control Circuits are useful and interesting. 🙏

[@Afumc]

Interesting circuit. This circuit simulates great in Tina with +/-5V rails, LMC6482 RRIO op amps, 2N3904 transistors and R = 10K. It also simulates fine with +/-12V rails, TL07x op amps, 2N3904 transistors, and R = 10K. On the other hand, don't expect to build it in real life with real parts and expect it to work as it is shown. I tried. In simulation, tweaking the value of any one of the 4 resistors marked R up and down by 1 percent shifts the offset all over the place. A couple of percent and offset is so far off, the circuit will not work. Maybe it will work OK as shown with 0.1% resistors and matched pair transistors. Or by adding trimming adjustment resistors all over the place which then increases complexity by a lot. Also, in real life, temperature compensating resistors may be needed to keep it from drifting with temperature.

[@STEMprof]

Glad that you like this video. Thanks for sharing your simulation results & observations. Matching Transistors & 0.1% Resistor are required. For more detailed design see Analog Computer Raises signal to Power of signal kzbin.info/www/bejne/h5aWlIxvf7itj8k I hope this unique power raiser circuit is interesting. 🙂

[@marcoluigi3066]

One question: because this circuit is better than the Gilbert cell? Thank you! (Interesting circuit)

[@STEMprof]

You are welcome! Thanks for watching and your good question. There are multiple ways to design analog multiplier including the famous Gilbert Cell architecture that you mentioned. For example see VCA Electronic Gain Control kzbin.info/www/bejne/mXfdio2phaqnhpI . Note that the 4-quadrant multiplier discussed in this video can operate with larger range of input signal (say up to +/5 or 10V) with less temperature sensitivity compared with the standard Gilbert Cell which mainly works with small signal. Note that it is possible to modify and enhance standard Gilbert Cell to improve its range of operation and also reduce its thermal sensitivity. In summary, the fundamental idea behind all these techniques is effectively similar since they all rely on the Shockley PN junction logarithmic V-I equation to implement analog multiplication or signal modulation. And yes, VT refers to the thermal voltage of the PN junction of BJT transistor. VT= kT/q where k is the Boltzmann constant and q is the electron charge. VT is equal to roughly 25mV when PN junction is at room temperature of 290 Kelvin. I hope this clarification is helpful.

[@marcoluigi3066]

@@STEMprof I tried to do a simulation with LTSpice and the circuit is ok with DC analysis. However, when I tried to multiply two sinusoids with the "transient" analysis (500mV/1KHz, 2V/50Khz) the result was wrong. I do not know why. I would have expected amplitude modulation.

[@STEMprof]

@@marcoluigi3066 Thanks for experimenting and sharing your circuit simulation observations. Did you use ideal Op Amp in your simulation? what type of transistor did you use in your simulation? what resistor values are you assuming in your simulation? For each op amp, I suggest that you add ~100 pf capacitor between the output of op amp and its negative input terminal (to further stabilize the circuit). After adding the capacitor, try your simulation again. I would suggest starting with (500mV/100Hz, 2V/5Khz) and if that works then increase the frequencies. As another related circuit example you might also like the VCA Electronic Gain Control: Voltage-Controlled Attenuator kzbin.info/www/bejne/mXfdio2phaqnhpI . I hope these are helpful.

[@marcoluigi3066]

@@STEMprof With 100pF it's ok, it just loses a bit of amplitude. (R=5k, BC547C, opAmp "Universalopamp2", single pole, +/- 15V power supply)

[@STEMprof]

@marcoluigi3066 Great! 👍 Glad that the feedback capacitor resolved the issue in your simulations. Now, please reduce it from 100pf to 20pf or 10pf. Does it improve amplitude performance?

[@lewisanesa1223]

Hi, did you try your design IRL? On simulation, even a variation of 0.2% of the most right hand resistor implies a variation of 25% on the output. I guess, then, that this design, in practice, may not have a good signal noise ratio...

[@STEMprof]

Thanks Lewis for watching this Analog Multiplier video and your follow-up simulation, good question and comment. This Op Amp BJT based circuit is an example to illustrate the core analog circuit concept showcasing one potential method of realizing analog signal multiplication. It is true that converting this to a real functional product with minimal sensitivity will require more circuit complexity and additional components. Thanks again for running the simulation and sharing your observations.

[@brunoluis2237]

working perfectly on simulation

[@STEMprof]

@@brunoluis2237 Glad that this Multiplier Circuit is useful. Here are related circuit videos: Analog Computer Power Raiser V1^V2 kzbin.info/www/bejne/h5aWlIxvf7itj8k Square Root Analog Computer Circuit kzbin.info/www/bejne/epTXZp-tht53q8U Analog Voltage Divider kzbin.info/www/bejne/aJLbemiiaMiZbMU Logarithm Amplifier (Log calculator analog circuit) kzbin.info/www/bejne/r367d62to9CSZ9k I hope these videos are interesting as well.

[@Neverforget71324]

This was one of my exam questions in college back in 1985.

[@STEMprof]

Test were surely more rigorous back then focusing on fundamentals and intuition. Glad that this circuit is useful. A few related Circuit Videos to see: Analog Computer Power Raiser V1^V2 kzbin.info/www/bejne/h5aWlIxvf7itj8k Analog Logarithm Computer with Op Amp kzbin.info/www/bejne/iKGudqRrjN6igsk Analog Exponential (Anti-Log) computer kzbin.info/www/bejne/oZyVlGp9oJihjZY I hope these videos are interesting as well.

[@fdvideoarchive9659]

Very good.Thank you.

[@STEMprof]

You're Welcome! Glad that you liked this Analog Multiplier Circuit. A few related Circuit Videos: Analog Computer Power Raiser V1^V2 kzbin.info/www/bejne/h5aWlIxvf7itj8k Analog Logarithm Computer with Op Amp kzbin.info/www/bejne/iKGudqRrjN6igsk Analog Exponential (Anti-Log) computer kzbin.info/www/bejne/oZyVlGp9oJihjZY I hope these videos are interesting as well. 🙋‍♂️

[@third_ear]

could a CD4049 be used in place of the op amps?

[@STEMprof]

Thanks for your interest. CD4049 is an inverting buffer from Texas Instruments. It can't replace an Op Amp. There are many cheap low-drift or zero-drift FET-input operational amplifiers from Texas Instruments or Analog Devices that can be purchased from Digikey or Mouser.

[@harrysvensson2610]

Who invented this analog multiplier? Or where did you find it?

[@STEMprof]

Thanks Harry for watching. This is my own 4-quad design and variation of the well known class and topology of Analog Multiplier. Is there a particular reason you're inquiring about that? The Analog Divider kzbin.info/www/bejne/aJLbemiiaMiZbMU among few more examples use nearly similar techniques. The general concept of using BJT or FET transistors in Darlington formation to realize analog multiplication has been around since the famous Gilbert Cell circuit back in 1960s. Analog multiplication is used in every cellphone to downconvert the received RF radio frequency signal carrier of few GHz to lower IF frequencies (in receiver) and upconvert IF to RF in transmitter so that data can be transmitted or received by the cellphones' tiny antenna. I hope this explanation is helpful.

[@wafikiri_]

I disagree with most of your equations, specifically almost all equations after equation (1) and before the final equation. Starting with that which you wrote at 7:40, iA=5/R. As the voltage difference is 5V., not the adimensional number 5, the equation should be iA=5V./R; what you wrote assigns iA the dimensional units of conductance, not of current, due to the ommision of the voltage unit. Consequently, also equation (2) is wrong, it should be 5V./R + V1/2R = I1. The same thing happens until the final cancellation of factors and terms. While the reasoning and the development of equations is right, their formal expressions aren't. And the only mistake recurrently happening is the ommision of the voltage unit, Volt or V., or its square Volt² or V²., from the expressions containing the adimensional numbers 5 or 25, thus depriving them the voltage or voltage square physical magnitude that they should represent. Anyway, thank you for this very ingenious and interesting circuit.

[@STEMprof]

Thanks for watching and sharing your thoughts.