Double Balanced Mixer - Very Linear ?

One of the Australian electronic magazines (EA, ETI, not sure) published a synchrodyne AM receiver in the 1970's using a quad CMOS switch, driven by I/Q outputs from a counter with a 4x VCO. Not very new...

Glenn put up some great stuff. Here's a link to rec.radio.amateur.homebrew is on this subject, a read thru that will give you plenty to think about.

Mikek

I can't visualise how that would be done in the diff pair of a Gilbert cell. If these transistors are run at constant current, how do they steer current into the upper stages?

Could you sketch it?

couldn't resist that one! Yes, it is difficult. I'm embarrassed to say has taken me over 2 months now [working part time on it is my only defense] As far as I know, I'm the only person to do this, ...so far.

It does have a limitation that you have to stay in 'reasonable' operation.

I could zip up a sample of the MC1496 modeled fairly well for an application I'm looking at. But the zipped file is somewhere between 30MB and 65MB, so NO way I can post that sort of wad of bits.

I work a lot in 0.001 Hz up through 1MHz, right now. so it has really helped to be able to 'add' in that pesky 1/f noise and watch it get replicated elsewhere WITHOUT the need to calculate what's going on [well, until later for verification].

Data sheet of the MC1496 shows it very well. The sample runs at bias of around 485u each so you can only 'tilt' approx 1/2 that before really start to see the distortion.

So how does it work?

Cheers

Phil Hobbs

On 4/4/2014 8:18 PM, RobertMacy wrote:

The MC1496 doesn't use the diode trick. Check out the LM13700 datasheet or the following listing.

Cheers

Phil Hobbs

Version 4 SHEET 1 1044 680 WIRE 112 -384 -96 -384 WIRE 368 -384 112 -384 WIRE 448 -384 368 -384 WIRE 112 -368 112 -384 WIRE -96 -352 -96 -384 WIRE 368 -336 368 -384 WIRE -96 -240 -96 -272 WIRE 112 -240 112 -288 WIRE 224 -240 112 -240 WIRE 368 -240 368 -256 WIRE 368 -240 288 -240 WIRE 112 -192 112 -240 WIRE 448 -192 112 -192 WIRE 368 -160 368 -240 WIRE 368 -160 240 -160 WIRE 112 -96 112 -192 WIRE 240 -96 240 -160 WIRE 368 -96 368 -160 WIRE 448 -96 448 -192 WIRE 48 -48 -160 -48 WIRE 176 -48 48 -48 WIRE 512 -48 432 -48 WIRE 640 -48 512 -48 WIRE 240 32 240 0 WIRE 448 32 448 0 WIRE 448 32 240 32 WIRE -160 48 -160 32 WIRE 640 48 640 32 WIRE 112 64 112 0 WIRE 368 64 368 0 WIRE 368 64 112 64 WIRE 576 96 -144 96 WIRE 720 96 576 96 WIRE -144 128 -144 96 WIRE 64 144 -32 144 WIRE 144 144 64 144 WIRE 576 144 576 96 WIRE 576 144 496 144 WIRE 720 176 720 96 WIRE 64 192 64 144 WIRE 240 192 240 32 WIRE 368 192 368 64 WIRE 576 192 576 144 WIRE 144 240 144 144 WIRE 144 240 128 240 WIRE 176 240 144 240 WIRE 496 240 496 144 WIRE 496 240 432 240 WIRE 512 240 496 240 WIRE -144 272 -144 208 WIRE -32 272 -32 144 WIRE -32 272 -144 272 WIRE -32 288 -32 272 WIRE 576 320 576 288 WIRE 720 320 720 256 WIRE 720 320 576 320 WIRE 64 336 64 288 WIRE 576 336 576 320 WIRE 240 368 240 288 WIRE 304 368 240 368 WIRE 368 368 368 288 WIRE 368 368 304 368 WIRE -32 432 -32 368 WIRE 304 432 304 368 WIRE 304 560 304 512 FLAG 64 336 0 FLAG 576 336 0 FLAG 304 560 0 FLAG -32 432 0 FLAG 640 48 0 FLAG -96 -240 0 FLAG -160 48 0 SYMBOL npn 176 192 R0 SYMATTR InstName Q1 SYMATTR Value 2N2369 SYMBOL npn 432 192 M0 WINDOW 3 -49 126 Left 2 SYMATTR InstName Q2 SYMATTR Value 2N2369 SYMBOL npn 128 192 M0 SYMATTR InstName Q3 SYMATTR Value 2N2369 SYMBOL npn 512 192 R0 WINDOW 3 78 98 Left 2 SYMATTR InstName Q4 SYMATTR Value 2N2369 SYMBOL current 304 432 R0 SYMATTR InstName I1 SYMATTR Value 3m SYMBOL npn 176 -96 R0 WINDOW 3 72 109 Left 2 SYMATTR InstName Q5 SYMATTR Value 2N2369 SYMBOL npn 432 -96 M0 SYMATTR InstName Q6 SYMATTR Value 2N2369 SYMBOL npn 48 -96 R0 SYMATTR InstName Q7 SYMATTR Value 2N2369 SYMBOL npn 512 -96 M0 WINDOW 3 -54 125 Left 2 SYMATTR InstName Q8 SYMATTR Value 2N2369 SYMBOL res 96 -384 R0 SYMATTR InstName R1 SYMATTR Value 400 SYMBOL res 352 -352 R0 SYMATTR InstName R2 SYMATTR Value 400 SYMBOL current -144 128 R0 WINDOW 3 55 -7 Left 2 WINDOW 123 24 108 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName I2 SYMATTR Value SINE(0 5u 1meg) SYMATTR Value2 AC 1 SYMBOL current 720 256 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName I3

SYMBOL current -32 368 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName I4

SYMBOL voltage 640 -64 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value SINE(2.5 500m 1.05meg 0 0 0) SYMBOL voltage -96 -368 R0 SYMATTR InstName V3 SYMATTR Value 5 SYMBOL voltage -160 -64 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V4 SYMATTR Value SINE(2.5 500m 1.05meg 0 0 180) SYMBOL cap 288 -256 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C1 SYMATTR Value 10n TEXT 560 568 Left 2 !.tran 100u TEXT -496 160 Left 2 ;Signal input (differential) TEXT 144 -296 Left 2 ;Output(differential)

if

I will dispute that with you analytically, perhaps even practically. For analysis purposes substitute as follows:

For Cos(nearly to real DC) the DC voltage; For Sin(nearly to real DC) 0 volts.

I got this from theory of limits. I presume that you have the ability to fill it in on your own from this.

Impressive, thanks!

-- Clifford Heath.

If the base band requirement is 0.001 Hz (and 1/f issues) I do not understand how you are going to transfer this on radio waves on SSB. At least a pilot tone (carrier) is absolutely required. Any Tx/Rx frequency error will destroy the low frequency accuracy.

I would suggest going digital with the DC to 1 MHz signal and then think about how to transfer it over radio waves (there are a huge number of alternatives).

Not at all. They are operating in the linear portion of the tanh(x) curve. They could not do the job at all if they were bouncing in and out of cutoff and saturation. They have to stay in the active region or create all kind of nasty non-linearities and harmonics.

BTW for all the people recommending saturated switching mixing, this is always followed be methods to suppress the harmonics generated. Which would likely reduce the accuracy of the measurements compared to not generating them in the first place.

Really? There are plenty of Gilbert cell multipliers that stay well balanced from DC to past 100 MHz. The Gilbert cell is all about the tanh(x) properties of differential pairs. That is the basis of how it works.

A barefoot Gilbert cell is a sorta-kinda multiplier. To make a good linear multiplier, you have to work quite a bit harder than that.

Gilbert cell frequency mixers are generally run with the lower stage linear and the upper stage switching. The upper stage works very much like a MOSFET- or diode-ring mixer. Switching mixers do give you intermod products of the form M*f_RF + N*f_LO, but you have to deal with that anyway, because even a 1%-accuracy multiplier only gives you ~40 dB spurious suppression, which generally is far too little. You deal with it by picking a good frequency plan and building good filters.

The crucial advantage of switching mixers is that they don't give you a lot of intermodulation between different signals on the RF port, i.e. they suppress spurs of the form M*f_RF1 + N*f_RF2. Lots of those wind up in-band, so filtering doesn't help nearly as much as a nice strong mixer.

And nobody in his right mind lets any of the transistors saturate. Saturation is slow and noisy, whereas cutoff is well-behaved. If you're running the Gilbert cell at, say, 3 mA total, then when the lower stage is in balance, each of the upper stage transistors switch back and forth from 1.5 mA to cutoff.

Sometimes, depending on what the input signal looks like. The first mixer in a receiver has a difficult life. Once you're past the first IF filter, life gets a lot calmer. In an instrument application, where you control what's in the input, you can sometimes design around the problem. But linear multipliers aren't that great, especially not quick ones. It's a lot easier to get 0.1% accuracy using a nice fast switching mixer than a Gilbert cell.

Of course it is. It just isn't linear _enough_, when there are strong interfering signals present. The Maclaurin series for tanh is

tanh(x) = x - (1/3) x**3 + (2/15) x**5 ....

For BJT pairs, delta I_C = I_tail * tanh(delta V_BE*e/(2kT)), so the scale factor is about 50 mV.

The third order term reaches 1% of the desired signal when the input amplitude gets up to

A properly designed linear multiplier does quite a bit better than this. The diode trick that I posted is one of the simplest ways of patching up the tanh characteristic, but there are lots of improvements you could add, such as cascoding the lower stage. In a vanilla Gilbert cell with sinusoidal LO, the lower stage collectors bounce up and down at twice the LO frequency, which is another source of nonlinearity.

For receivers, there are other things that might be useful:

It would be sort of interesting to try replacing the lower stage of the Gilbert cell with a center-tapped transformer secondary.

In a MOSFET bridge, it might be better to give each of the FETs its own LO winding, connected G-S as in HV SMPSes. Driving the gates in pairs gets rid of the even order distortion terms but not the odd order ones, whereas separate gate drive should pretty well get rid of both.

Cheers

Phil Hobbs

Ahmm... lets be accurate shall we... :-)

The basic multiplier is the "Howard Jones cell" invented by said person in

The true Gilbert Cell is the the Howard Jones cell with logging diode (transistors) on the input. It is the logging bit (aforementioned trick) that Barrie introduced to get, in the ideal limit, perfect multiplication.

So, in reality, the Gilbert Cell is actually very linear, assuming a decent V-I converter feeding the diodes. It is the Howard cell that is nonlinear.

Kevin Aylward B.Sc.

it's

LO never was a worry, the 9 decades band on the input was the bother. Gettting 90 degrees over more than three decades (from a single source) is all but impossible.

That said there are multipliers that are good from DC to 250 MHz or more.

I do not always like square wave drive on diode rings because of the harmonics which are usually just filtered out but that doesn't seem like it would work in your application as stated so far.

If you can keep f(m)

Wow!

That appears quite a bit more 'linear' than the MC1496. Can you confirm that it is?

Sure. The 'diodes' are running at a dynamic impedance of around 250 ohms, so replace them with 250 ohm resistors and run an apples-to-apples comparison.

Cheers

Phil Hobbs

I don't think I understand. I removed Q3 and Q4 and replaced them by 250 ohms to ground, and I can see no significant change in either the waveform or the FFT.

Clifford Heath.

The leading-order nonlinearity is cubic in the signal current, so try stepping that and see what happens in each case.

Cheers

Phil Hobbs

Phil, there is NO magic in what I did. Simply brute force...'add' the appropriate noise source(s) to every 'important' component. But you saw that already, right?