Electronic – Gilbert cell biasing

biasgilbert-cellmixerschematicstransistors

I'm new here so I'm going to make is as simple as it can get..
How can I bias a Gilbert cell with bjt transistors like this one:
Basic Gilbert cell schematic
What methods can I use to bias the transistors? Is there any example schematic where they show how biasing resistance are put and calculated?

I've tried many methods but I got stuck, because I suck at dealing with transistors since uni days.. For instance, I could bias the diff amps with base resistance method, like this one:

base bias

but got stuck in biasing tail transistor since it's its collector is linked to the upper diffs emitters rather than +vcc like in this example:

tail tran

I may have done my research in the wrong way, but I've looked in many articles, files etc even in different languages, but all I can find is basic gilbert cell theory and that's it, I managed to find only one practical example so far.

Please, I'm getting really desperate, I've been stuck with this for a very long time now, the place where I live, electronic devices are really limited, I can't find mixers in any shape or form, IC mixers, or even toroid to make a diode ring mixer since it's simpler. All I have is only 2N2222A transistors that could operate up to 300 MHz, so they're my only way. I appreciate any type of help, advice or information you can give me.

Best Answer

Well guys thank you all so much for your help, I immensely appreciate it!!

Well while discussing the matter in the comments with jonk (thanks for the link) and Marcus Müller, I had the idea of simply treating the upper diff pair as a simple load that has 20mA through, and made a voltage divider biased current sink, and calculated the resistance values with the same method of biasing a base divider biased common emitter biased amplifier, and with simulation i got mixed signal.

So here's a recap:

i biased the upper pair with simple base resistance biasing method I made the following circuit:

schematic

simulate this circuit – Schematic created using CircuitLab

Well I wanted my Q point for each transistor to be 6V, 10mA, for that the value R1 and R2 is 600Ohms, and to make sure that the base runs with ic/hfe (with hfe around 200) R3 and R4 have 226kOhms.

Now thanks to the discussion I've had with the guys i thought about treating the whole block as a load itself that requires 20mA, therefore i added the following circuit instead of the constant current source:

schematic

simulate this circuit

And what i obtained from the simulation (Multisim) is the following:

enter image description here

(sorry didn't know how to resize it) The expected results are shown, and it's the same situation for the Gilbert made out of this simple balanced mixer.

Only 2 issues bother me, the 226k resistance (very high value) I'm wondering if i can remove it or not.. and inputs need to be very small..

theory behind it as well as schematics can be found on: http://michaelgellis.tripod.com/gilbert.html and the link jonk proposed: https://smallwonderqrp.blogspot.com/2016/02/home-brew-your-own-mixer-ics.html

So how catastrophic does this look?? And what do you guys think? Please be gentle haha