R.F. Mixer: Gilbert Cell vs half'ish Gilbert Cell

Thread Starter

retiredEE

Joined Nov 14, 2019
13
One of the standard mixer topologies is the Gilbert Cell which amounts (greatly simplified) to a pair of stacked differential amplifiers. If we are feeding this from an unbalanced source, then one half of each of these dif-amps is essentially unused while the other half does all the work.
So, my theory is that the same thing can be done with a simple stack of three transistors.
- The bottom is used as the current source.
- The center is the L.O. input.
- The top is the signal.
My simulation model seems to work exactly as I expect it to work.
With this great simplification and the fact that the Gilbert Cell is so ubiquitous, I am thinking that there is a good reason NOT to use my simplified version.
Can someone enlighten me on this?
 

Bordodynov

Joined May 20, 2015
2,491
I don't agree with you. With asymmetrical signals, Gilbert's cell works all the way through. Look at my example. I have drawn transistor currents on the diagram.
Half of the circuit will work if you intentionally close one of the lower transistors.2019-11-15_08-50-36.png
 

DickCappels

Joined Aug 21, 2008
6,175
@retiredEE I am curious about the biasing. Would you please post the schematic of your simulation?

@Bordodynov I see that in some applications the loss of the out-of-phase signal could result in a noise issue, but other than that do you see any problems with retiresEE's approach?
 

SLK001

Joined Nov 29, 2011
1,543
Almost any semiconductor will mix two signals and give you the COS (a+b) and COS (a-b) signals. The problem with this mixers, is it will also give you most of the unwanted signals, ie, COS (2a+b), COS (3a-2b), etc. The "balanced" in a double balanced mixer minimizes these "rogue" signals, making post mix filtering easier (and even possible). Many of the rogue signals will fall in your desired passband, making post mix filtering impossible. That's why you design your mixer to minimize these, thus that's why a double balanced Gilbert Cell mixer is used.
 

Thread Starter

retiredEE

Joined Nov 14, 2019
13
Well ... maybe I just answered my own question. L.O. = 10 MHz. Signal input = 33 MHz.
Using LTspice, I simulated three approaches: my "half-gilbert", the full Gilbert driven single ended and the the full Gilbert driven balanced via center-tapped xfmr. I exported the data and did a Fast Fourier Transform on the data using EXCEL. While the frequency buckets did not line up very well with each other, I saw what I needed to see.
The half-Gilbert did a great job of reproducing the original two signals, it did nothing in the way of mixing. It was more of an adder than it was a multiplier.
Both full-Gilbert versions did exactly what they should do. The one driven balanced with center-tapped transformers has a "cleaner" spectrum. All this in simulation ... no real hardware ... yet.Mixer-Gilbert Cell.xlsx - Excel 11_15_2019 8_54_53 AM.jpg
 

Thread Starter

retiredEE

Joined Nov 14, 2019
13
Almost any semiconductor will mix two signals and give you the COS (a+b) and COS (a-b) signals. The problem with this mixers, is it will also give you most of the unwanted signals, ie, COS (2a+b), COS (3a-2b), etc. The "balanced" in a double balanced mixer minimizes these "rogue" signals, making post mix filtering easier (and even possible). Many of the rogue signals will fall in your desired passband, making post mix filtering impossible. That's why you design your mixer to minimize these, thus that's why a double balanced Gilbert Cell mixer is used.
Good point! And, as you can see in my post, I actually proved that to myself by simulating both the unbalanced and balanced approach to the Gilbert Cell. The balanced approach yields a MUCH nicer output spectrum.
Thank you for your reply. :)
 

SLK001

Joined Nov 29, 2011
1,543
You're not getting a true simulation of the mixer. LTSpice is a simple linear simulator. To properly simulate a mixer, you'll need a non-linear simulator, like ADS or similar. If you use a non-linear simulator, you'll see just how ugly a non balanced mixer can be, and how hard it is to get a true balanced input and load for a mixer. When we were doing Ga-As mixer designs, the lines leading up to the cells (on the chip itself) were exactly the same length. Even slight variation of the lengths caused enough phase variance to completely screw up the desired output. Every time we changed foundries, or technologies, we had to redesign the mixer.
 

Thread Starter

retiredEE

Joined Nov 14, 2019
13
You're not getting a true simulation of the mixer. LTSpice is a simple linear simulator. To properly simulate a mixer, you'll need a non-linear simulator, like ADS or similar. If you use a non-linear simulator, you'll see just how ugly a non balanced mixer can be, and how hard it is to get a true balanced input and load for a mixer. When we were doing Ga-As mixer designs, the lines leading up to the cells (on the chip itself) were exactly the same length. Even slight variation of the lengths caused enough phase variance to completely screw up the desired output. Every time we changed foundries, or technologies, we had to redesign the mixer.
WOW! Great advise! This will help me when I build actual hardware ... keeping trace lengths precisely the same. Hard to do when one is hand winding toroid transformers.
I am assuming this is more critical with higher frequencies (?). Initially I am going to build a single conversion receiver for the 40M (7MHz) band as a learning project. Ultimately I am looking at a 450MHz (70cm), FM receiver. I may "cheat" and use one of those often used NXP devices instead of discrete components for the LO and mixer.
Unfortunately, ADS (a Keysight product) only has a 30 day free trial. Being retired now (and cheap, too) and a non-professional experimenter, it would be hard to justify the big bucks I *assume* the full simulator would cost (quick check with Keysight ... $37K!). Are there cheaper options? dunno where to start looking.
 

SLK001

Joined Nov 29, 2011
1,543
Use bifilar wire when hand winding toroids. The higher in freq you go, the more important keeping lengths well controlled are.
 

Thread Starter

retiredEE

Joined Nov 14, 2019
13
Use bifilar wire when hand winding toroids. The higher in freq you go, the more important keeping lengths well controlled are.
Now ... if I am winding a simple inductor, is this the application of what you speak?
I was planning on a trifilar winding for my transformer for the mixer. This way I can use the "center-tap" of the secondary to apply the transistor bias.LTspice XVII - [Mixer-Gilbert Cell with xfmr.asc] 11_15_2019 5_26_37 PM.png
 

SLK001

Joined Nov 29, 2011
1,543
You would be better served if you purchased your matching baluns from Coilcraft, Mini Circuits or Murata, etc. They have the equipment to verify proper operation. They aren't that expensive and the time and headache that they will save can make purchasing them worthwhile.
 

SLK001

Joined Nov 29, 2011
1,543
LTspice is a complete tool and can be used to calculate radio frequency mixers.
Not really... LTSpice is a linear simulator and can give you a pretty good estimation of the 1st and 2nd order mixing products - that's all. To completely characterize a mixer, you'll also need the 3rd, 4th, 5th, 6th and 7th order mixing products, some of which can be quite strong and appear in the passband of your desired IF. No amount of post-mix filtering can eliminate the undesired signals in your passband - they must be minimized by mixer design. This is why weird frequencies are used for IF frequencies, ie, 10.7MHz (why not a simpler 11MHz?) for FM broadcasting receivers, 455kHz (why not a simpler 450kHz?) for AM receivers, or 73.35MHz (why not 73MHz, or even 70MHz?) for some FM transceivers. In fact, a receiver IF is selected after a mixer has been designed and evaluated. It is selected so that the majority of higher order interfering mixing products will lie outside the IF passband. The 7th order products are called the Alpha-Baker responses and are usually a big concern to receiver designers.
 

Thread Starter

retiredEE

Joined Nov 14, 2019
13
Not really... The 7th order products are called the Alpha-Baker responses and are usually a big concern to receiver designers.
I am learning a LOT from you!
When it comes to R.F. design, I am a neophyte and, admittedly, have a LOT to learn. I am in the process of trying to learn more and the nuances of practical RF design is the stuff you do not find on the Internet or, sadly, in books. I am awaiting two books (LOTS of money!) which I hope will help.
I do have a calibrated VNA and a spectrum analyzer, so I am not without equipment to see what is really going on. Knowing what to look for and how to use this stuff to look for it is a BIG part of what I am learning. I have no one to teach me, so great advise like yours and a lot of hands-on experimentation is in the future.
Part of my learning curve is trying for myself and seeing the results. In the end, purchasing the Coilcraft parts is most likely where I will end up to cement the best performance. The first stab at it, however, will likely be with hand-wound transformers ... that's part of the fun of it all.
 

Bordodynov

Joined May 20, 2015
2,491
Not really... LTSpice is a linear simulator and can give you a pretty good estimation of the 1st and 2nd order mixing products - that's all. To completely characterize a mixer, you'll also need the 3rd, 4th, 5th, 6th and 7th order mixing products, some of which can be quite strong and appear in the passband of your desired IF. No amount of post-mix filtering can eliminate the undesired signals in your passband - they must be minimized by mixer design. This is why weird frequencies are used for IF frequencies, ie, 10.7MHz (why not a simpler 11MHz?) for FM broadcasting receivers, 455kHz (why not a simpler 450kHz?) for AM receivers, or 73.35MHz (why not 73MHz, or even 70MHz?) for some FM transceivers. In fact, a receiver IF is selected after a mixer has been designed and evaluated. It is selected so that the majority of higher order interfering mixing products will lie outside the IF passband. The 7th order products are called the Alpha-Baker responses and are usually a big concern to receiver designers.
LTspice - Spice simulator. And it is not a linear simulator. Linear simulator will not give any harmonics! Neither the second nor the third one. If you look at the input currents of the transformer (spectrum), there will be all harmonics. Moreover, that in my example absolutely identical transistors are used, and in a reality there will be some asymmetry. I also have an ideal, symmetrical transformer, but in reality it is not. Unfortunately, I have a diagram of my example on my office computer and I can't (I don't want to be lazy to reintroduce it) on my home computer. But tomorrow I will output the spectrum of currents through the outputs of the chip so that you can see higher harmonics and change your mind about LTspice. I can also introduce some asymmetry and show that the harmonics will become bigger.
 

Bordodynov

Joined May 20, 2015
2,491
Here I keep my promise and output the results of Fourier transformation for the output current through pin number 3 of the chip on the diagram. I can see a lot of harmonics.

2019-11-18_07-41-28.png
 
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