Some Analog IC Gilbert Cell Mixer Notes

 Introduction

Updated April 2, 2023 — scroll to the bottom for addendum

I love working with analog ICs. For example, op-amps, sensors, audio PA chips — and of course the parts we apply as modulators/demodulators and mixers for frequency translation. Analog ICs using BJTs or MOS devices tend to contain 3 main components: [1] differential amplifiers [2] various types of emitter or source followers [3] constant current sources. In the case of bipolar transistors (which I'll write about), I use the terms emitter-coupled pairs (ECPs) and differential pairs interchangeably in this blog post.

Let’s focus on frequency translation with the so-called four quadrant analog multiplier that many refer to as the Gilbert cell mixer. Others may call it the Jones-Gilbert mixer since H.E. Jones had patented a similar layout prior to B. Gilbert’s 1968 paper [Reference 1]. 

It’s called 4 quadrant because in addition to 2 outputs, there are 2 inputs (X and Y) with 4 possible differential signal combinations: +X, +Y;  -X, +Y ;  -X, -Y and +X, -Y  where +/- refers to the polarity of the AC waveform at the LO and RF inputs. A mixer switching transistor switches to an open or closed state by the polarity of the AC LO signal applied to its base.

Gilbert Cell Pros/Advantages

• RF to IF Conversion gain with double balance ( the main reason to use them )
  
• May have wide bandwidth in newer design monolithic ICs
• Eliminates common mode noise

Gilbert Cell Cons/Disadvantages

• More flicker noise than passive ring topology mixers which typically offer better low frequency noise performance

Devices including semiconductors exhibit low frequency noise that is inversely proportional to frequency that’s called 1/f, flicker, or contact noise. 1/f literally means flicker noise is greater when frequency is lower. In the case of BJTs, this low frequency voltage fluctuation (noise) likely gets produced when base current flows through the rbb or base spreading resistance of the mixer ECPs and interacts with microscopic contact + surface imperfections in the substrate.

Flicker noise adds to the mixer noise figure and proves even more vexing with direct conversion architectures since these mix down to audio frequency — and any low frequency base band noise (such as flicker noise) gets amplified in the audio signal chain. Flicker noise is worse in Metal Oxide Semiconductor (MOS) transistors than in BJTs [Reference 2].

Modern Gilbert cell mixer engineers toil relentlessly to reduce flicker noise / mixer noise figure at very high frequencies.

Gilbert Cell Cons/Disadvantages continued...

• A narrow bandwidth in earlier monolithic ICs.
• Lower dynamic range than passive ring topology mixers
• Many of the older and now obsolete designs ran low power [low DC voltage(s) and/or current] — so they suffer from low IP3 and dynamic range. There were exceptions such as the venerable Plessey SL6440.

I do not make superheterodyne receivers and instead focus on the direct conversion architectures of zero-IF or low-IF. Thus, an IC such as the SA612 would make a poor choice for me on the Ham bands since I like to listen to CW pileups on contest weekends where in amongst weak signal clusters lie abundant strong signals that would invariably overload my low power IC product detector(s) and make me feel sad. 

Then, too, an analog Gilbert cell IC might be OK for use in a DC receiver used to study the atmosphere or listen to decametric emissions from Jupiter.

 Double balanced

The Gilbert cell mixer is double balanced for LO and RF so, ideally there should be no LO or RF leakage into the outputs. In reality, port isolation isn’t perfect and factors including BJT matching and single-ended versus balanced LO & RF inputs may affect port isolation along with other mixer parameters such as IP3. However, the Gilbert cell mixer does not just rely on transformers to give balance; therefore, it still functions as a double-balanced mixer whether you use single-ended or differential inputs on the LO and RF ports

Mixer balance affects port to port isolation and more. When unequal currents flow in an ECP, overall cancellation is reduced. Symmetry is everything in balanced mixers — common mode noise, input signals & even order harmonics alike get reduced in amplitude through precise 0 to 180 degree phase shift cancellations within the ECPs of the Gilbert cell mixer. 

Going… going… Gong!

Many classic Gilbert cell monolithic IC mixers lie obsolete. These include the MC1496, MC1595, IAM-81028, SL6440, µPC1037, SOP42, TL-442 and AN612. The NE/SA 602 or 612 chip is still available but must be circling the drain at this point. Still in production IC packages range from the simple HFA3101BZ96 to the ADL5801-5802, ADL5380 (I/Q demodulator), MAX2680-MAX2681-MAX2682, SMA5101 and many others.

Like they say — “if you like an analog part now, buy some today because they might not be around in the days past tomorrow”. It's worth reflecting that industry needs dictate the rise & lifespan of parts. Hams and hobbyists latch on to certain parts while in production and well after they turn obsolete —but it was never about home brew electronics.

Modern builders have employed Gilbert multiplier cell mixers into mm-waves in industry or research. Apart from BJT and MOS devices, in microwave you might see monolithic microwave integrated circuit (MMIC) implementations in InP HBT, SiGe HBT, GaAs HBT and pHEMT high speed technology.
Modern Gilbert cell mixers typically employ low DC voltage, low to moderate current and very high speeds.

Predistortion and improving linearity in the ECP

Barry Gilbert’s version of the 4-quadrant analog multiplier predistorted the LO input signal of the switching transistors by essentially using diodes to compress the signal logarithmically. From his 1968 paper describing his experiments, the terms Gilbert cell or Gilbert mixer arose to popularity [Reference 1].

For amateur radio buffs, we may eliminate his linearizing predistortion circuitry plus any DC offset balancers since as a RF mixer we employ high Q, tuned band-pass circuitry to remove unwanted frequencies — and as a product detector we use a low-pass filter network to remove any residual carrier and other RF garbage that leaks through to the zero-IF or low-IF output(s).

The 4-quadrant multiplier proves a versatile analog workhorse circuit

The versatile 4-quadrant multiplier may be set up to function as a squarer/multiplier, divider/square rooter, frequency doubler, balanced modulator or demodulator for AM or SSB, an FM quadrature detector and a variable gain control amongst other tasks. A true analog workhorse circuit.

Gilbert Cell Mixer Function

Let’s examine basic mixer function.

Above — The basic structure of the Gilbert cell mixer. LO is applied to the X ports and RF to the Y ports.

The switch quad (sometimes called the mixer core) Q1- Q4 multiply the linear current from Q5 and Q6 with the switched LO signal.  Q5 and Q6 provide +/- RF current and Q1 and Q4 switch alternately to provide normal or inverted output to the Q1 load resistor while Q2 and Q3 switch alternately to drive the Q4 load resistor with a normal or inverted output.

Switch quad [ Q1-Q4 ]

 2 cross-coupled, parallel, differential BJT pairs form a quad switch

• Q1 & Q4, then Q2 & Q3 function as differential pairs within the quad
  
  
• The 4 upper transistors go either fully ON or fully OFF in response to LO polarity at each half-cycle of the LO waveform
  
  
• The quad switches multiply the current from each collector of Q5 & Q6 by +1 or -1. Multiplying the RF signal by +1 transfers it to the output with no phase change, while multiplication by -1 inverts the output 180 degrees in phase
  
  
• When the LO signal goes positive in polarity, Q1/Q4 turn ON and Q2/Q3 turn OFF. This flip flops when the LO cycle goes negative in polarity. No change in current occurs in Q5 and Q6. Due to their symmetry, the 2 current arms I-1Y and I +1Y lie equal and opposite — and thus cancel out
  
  
• 1 collector output node will always receive the negative of the current value at the other output node
  
  
• The ideal drive for the upper transistors is a differential square wave of about 0. 9 Vpp. If fed with a sine wave, then Vpp should run about double or triple the 0.9 Vpp square wave amplitude to create a switch quad conductance waveform that mimics a square wave
  
  
• In short, ensure that you apply enough LO amplitude to switch the upper transistors ON and OFF quickly
  
  
• Ideally feed the quad switch from a low-impedance LO signal source, although that’s not critical.  A virtue of the Gilbert cell mixer is that it’s not as fussy about port impedance as a diode ring mixer. You may require quad switch base termination resistors to allow stable drive from your LO signal source. For example; with a single-ended LO input 

Transconductance pair [ Q5, Q6 ]

• The 2 lower transistors operate linearly like standard differential amplifiers on the RF input signal to convert the RF input voltage into current for the commutating switch quad above

• For the RF signal path to the lower pair, any base termination such as low-value resistor bias resistors may take away RF signal power from the lower ECP.  Base bias resistor values should generally only be as low as required to insure a stable DC bias voltage

• In IC data sheets, you’ll observe bias resistor values from 120 to 3K3 Ω in single DC supply designs, while several thousand Ω resistors may go from base to ground in split DC supply designs. Experiments and simulation may help you choose your ideal resistor values. Some designs match the lower RF pair input impedance to their RF source Z to boost conversion gain. 

Simple bias resistor versus constant current source

The ideal current source offers a fixed current level, a high output resistance, & low noise.

Figure 2 for Discussion    Figures A to D show the (lower 2) simple differential amps with a split DC supply for clarity.

For maximum real-world performance, IC designers use ECP’s matched for VBE and hFE (Beta). That’s much easier to do when the transistors come from the same substrate. If you choose to build a Gilbert cell from discrete BJTS — indeed, you should match the discrete transistors that make up your ECPs. 

With some ICs, you'll decide whether to use a plain old emitter resistor to provide ‘constant current’ to your mixer, or to employ a constant current sink device: a transistor biased with resistors and/or diodes, or used to mirror a separate reference current.

In Figure A, RE is a simple resistor and the current flowing through the ECP is determined by -VEE and RE. The sum of the currents flowing through each ½ of the ECP should ideally be fixed or constant. In order for that to happen, RE must be a large value resistor to drop a significant voltage across it. 

This means the corresponding DC voltage must also be large. Typically, most builders run lower DC voltages such as 5 to 12 volts with a single power supply rail. Thus, RE falls short as a constant current source whether running single or split DC supply. It might be perfectly OK to run RE in bench design work, for low complexity radios, and/or at very high frequencies. 

Figure B shows RE replaced by a transistor Q3. We assume that the collector to emitter current of Q3 is equal to the base to emitter current X the current gain of the transistor & its current gain is independent of the collector to emitter voltage.

Figure C shows Q3 fully biased from the negative rail with included diodes to boost temperature stability. Since the diodes get fabricated from the same wafer, they thermally track the ECPs and offset temperature-related current changes.

While Figure C is OK, some constant current sources are better than others. A basic, better-grade and popular constant current source biased with positive DC is shown in Figure D. This circuit is known as a current mirror and a ‘diode-connected’ BJT (Q3) forms the current mirror. Just like ECP’s, both current mirror transistors need matching for best results.

Various forms of improved current mirrors exist and include for example, the Wilson and Widlar current mirror designs. You may see emitter resistors on both transistors to help with transistor matching and to raise the effective collector resistance. Finally, please refer to Figure E to see cascaded current mirrors in use with a Gilbert cell mixer. An example of this lies in the MC1496.

Input signals common to both differential amplifier inputs (common mode signals) such as noise, or stray voltages that drive both inputs will not get amplified since this is a difference amplifier. In effect, the differential pair rejects common mode signals — and the better this rejection, the better the balance of the differential stages are in the amplifier or mixer. Thus, DC current through mixer ECPs should ideally remain fixed no matter what— and a constant current source helps achieve this. Other Gilbert cell mixer constant current source benefits might include improved output linearity, boosted port isolation & potentially reduced power rail noise.

Thus, a constant current source marks a big improvement over the plain old resistor RE. Summarized --- For an ECP, the higher the resistance of its current source, the lower the common mode gain + the better the common mode rejection ratio.

I have merely scratched the surface about constant current sources. Abundant constant current source info lies in books on differential amplifiers + constant current sources and on various web sites.

Balanced or unbalanced input and/or output

We’ve got decisions to make. Considering the external RF or LO stages that drive our Gilbert cell mixer – plus whatever stage is going to receive the mixer’s output, we’ve got the following choices:

[1] LO and RF Mixer Input Ports 

• single ended LO and RF output to single ended mixer LO and RF input
• single ended LO and RF output to differential mixer LO and RF input
• differential LO and RF output to differential mixer LO and RF input
• a hybrid combination – different drive strategies for the LO and RF ports

A lot of choices!  Once again, you’ll decide how you feed your LO and RF ports. Single ended inputs ranks as very popular with home builders. Myself, I prefer differential LO & RF drive using a balun transformer with the primary to secondary turns ratio providing the input match to the RF and LO single-ended signal sources. The SA612 and ilk data sheet has a wonderful section showing the various ways to input signals into a Gilbert cell mixer. I recommend you download this data sheet along with the data sheets of the other IC mixers I have mentioned in this blog post. Data sheet study remains a proven way to learn more about electronic devices + circuitry.

[2] Mixer Output Ports

• single ended output off 1 collector
• differential output using both collectors to either a single ended or differential post- mixer input stage
• collector resistors versus transformer for the output whether single ended or differential output
• broadband versus tuned collectors if using an output transformer

I favor differential output using a center-tapped transformer which doubles your output power over a single ended output. However, then you’ve got to make or purchase a center tapped transformer that will also step down the high collector impedance to something close to your post transformer device input impedance. This might even involve you winding a trifilar transformer on a ferrite toroid.  Many experimenters evidently suffer an inflammatory disease known as TTA [ Trifilar Transformer Allergy]. For them, a trifilar transformer crosses the line.

Wouldn’t it be easier to just apply a simple resistor to convert that collector current into a voltage and then not have to mess with a transformer? Yes. There are always trade-offs — plus your needs may vary. What are you using the mixer for? If it’s just a transmit mixer, I may just use a resistor and feel OK with dropping my conversion gain by half. But that might not be OK for a receiver. Since a major reason to employ a Gilbert cell mixer is to get mixer conversion gain, I tend to go with differential output to either a single ended or differential input next stage in my receivers. Your needs may vary.

 Datasheet Studies

Let’s dive in.  I’ll briefly show 3 data sheet examples that illustrate single supply DC biasing with or without constant current sources and various mixer input and output strategies.

Recall that the RF enters via a differential transconductor with their output currents commutated by a quad of LO switches. The top switch quad operates in the saturation region while the bottom ECP are biased in their linear region.

Above — The data sheet schematic of the S042P Gilbert cell IC.  No constant current source. Typical current consumption = 2.15 mA. No internal switch quad collector resistors are provided. The resistors and diodes shown above are contained in the substrate.  The builder supplies external bypass/signal capacitors, gain setting resistor(s) for the transconductance pair current — and AC connections through coils for the RF, LO and output in typical applications.

This DIP-14 IC mixer offered by Siemens Semiconductors (Infineon) ran a maximum DC voltage of 15v and went to 200 MHz.  It featured an optional built-in oscillator. The data sheet shows a NF of 7 dB. They also offered a round, leaded, metal case version called the SO42E. You’ll see this IC in many European home brew gear, including the projects of LF and VLF enthusiasts in more recent times. The oldest schematic I could find using the S042P was dated 1979.

Using an 8K2 instead of an 8K resistor, I show the upper quad plus lower ECP DC bias voltages using a bench DC supply of 12.18v. The entire bias stack consumes 1.2 mA. The wafer fabricated bias diodes are thermally matched to the ECPs in this IC for temperature compensation. This data sheet shows an archetypical way a builder may bias a discrete transistor Gilbert cell mixer. Each diode in the bias stack drops ~ 0.61 VDC.

The diode pairs may be replaced by fixed resistors and biasing via resistor voltage dividers plus the 2K2 and 3K3 decoupling resistors remains common in home brew BJT Gilbert cells built today.

Since the transistor fT’s were high (probably >=1 GHz), VHF oscillations often occur. They suggest a 10-50 pF capacitor between the LO inputs to prevent VHF parasitic oscillations. Other builders implemented low value series resistors on the ECP base inputs as well.

Above — A data sheet schematic of the HFA3101 Gilbert cell IC with some DC bias values added by me. No constant current source. Absolute maximum current consumption = 30 mA. This is just a very fast transistor array with a small PC board footprint. The builder supplies all biasing resistors, capacitors, & current setting + degeneration resistors for the transconductance pair — and AC connections through resistors, caps, and/or coils for the RF, LO and output.

This SOIC-8 IC mixer offered by Renesas specifies an fT of 10 GHz. It’s tiny and fast using BJTs!  A review of the data sheet proves fascinating. This part appears well characterized for 50 Ω use and the circuit examples give clues how we can set up our own discrete or IC mixers using single-ended inputs and outputs. The singled-ended LO + RF input penalty of reduced port isolation is acknowledged in the data sheet and it well shows the trade-offs builders must consider.

At high frequencies such as UHF, they specify that the LO must be matched to the switch quad input to avoid parasitic oscillations. RF port matching also proves important for conversion gain. Clearly a mixer operating as a upconverter @ 825 MHz is a whole different animal from a HF Gilbert cell mixer. The design examples show very low value biasing resistors — again this is for UHF and I estimate the low values may provide stable bias, low noise, low input impedance and decreased potential for parasitic oscillations. My added notes show a VCC of 2.96 VDC. I swapped a 120 Ω resistor for the 110 Ω resistor shown. DC bias voltages are shown for the upper quad and lower ECP — the total current draw of the bias stack alone = 4.4 mA due to the low value bias resistors.

The RF capacitor values shown don't make sense. The series resonant frequency of the 0.01 µF caps shown seems too low for UHF applications.

Also mentioned in the data sheet, when a (single-ended) output tuned coil is shunted with a 2K resistor, this improves the third order intercept while somewhat decreasing gain. E.g. less distortion products are generated while stability is enhanced. This would be something to try at HF on your test bench if you’ve got the test gear and want to run a tuned, single ended output.

You really go to school by reading this data sheet. What a fabulous IC that doesn’t use MOS transistors — so we can relate to it a bit better.

Above — The schematic of the silicon BJT MMIC IAM81008 Gilbert cell IC offered in the past by Hewlett Packard (Keysight Technologies). Single polarity bias supply of 4 to 8 VDC [ most often builders would use 5 volts which would draw a maximum DC current of 12 mA.   SSB NF = 17 dB. RF and LO ports = 50 Ω.  8 dB RF to IF conversion gain from 0.05 - 5 GHz with an IF output from DC to 1 GHz.

This is a great historical example of a complete, active mixer that required minimal off-chip parts to get it operating at VHF to UHF -- plus it also featured an interesting on-chip bias circuit.  You just need to AC couple in your RF plus LO signals with appropriate value capacitors -- and then provide a VCC and ground. Pretty amazing active 5 GHz IC mixer in that day in time.

As such, this double-balanced mixer was used with single-ended LO + RF and output ports. A built-in emitter follower reduced loading effects on the output port, The current sources schematic numbered 1,2 and 3 show the evolution from a typical on-chip current mirror to something much more sophisticated.

This mixer seemed popular for VHF and UHF work in Europe for experimenters and while it suffered from a relatively high NF (lots of transistors + resistors) and low dynamic range, it worked OK as second mixer in a typical receiver -- or perhaps as a transmit or PLL mixer.

Many writers have covered the SA-612 and ilk, so I won’t.  For me, a measured SSB NF of <=  ~8 dB at <= 45 MHz made that part special when it came out. However, modern Gilbert cells ICs offer a much improved dynamic range plus a higher upper frequency limit —  although they’re not as easy to use for HF to lower VHF home brew experiments as the popular SA612.  

Home brew Gilbert cell Mixers

Although this blog post covers analog ICs, I'll write a few comments about making home brew versions with discrete transistors. I've built at least 6 discrete BJT home brew Gilbert cell mixers and each of them suffered strong parasitic oscillations between 110 to 430 MHz. Whether using single-ended or differential inputs or output, they oscillated. When running higher currents such as > 12 mA to get a better input intercept, parasitic oscillations tended to worsen. Some mixers were stable with 1 set of LO and RF input frequencies, but then became unstable when used with different LO and RF input frequencies. Quite vexing.

I had to spend a lot of time adding series resistors, bypass capacitors and so forth to swamp out these VHF-UHF oscillations. The whole process proved time consuming and frustrating. With commercial, analog IC versions, I did not suffer these problems, or they were easily fixed if parasitic oscillations happened to arise.

I can make a simple, stable, active, transformer-balanced home brew mixer with 2-4 FETs or BJTs that will outperform any of my discrete transistor Gilbert cell mixers with far less parts and stress. Thus, I tend to use commercial IC Gilbert cell mixers.You may have better luck!  Perhaps, I'm doing something wrong?

Above — A spectrum analyzer screen shot of the output of 1 of my better home brew Gilbert cell mixers. RF = 14.08 MHz @ 0 dBm input, LO = 9.98 MHz @ 0 dBm input. This was for a down conversion mixer to a 4.06 MHz IF.  RF conversion gain = 16.35 dB. I've measured as much as 19 dB conversion gain in my home brew Gilbert cells once parasitic oscillations were stifled. The LO and RF signals are down ~ 32 dB which shows pretty good balance for a home brew Gilbert cell mixer. You can see other strong tones in this image, but those are pretty standard in RF mixers. This was an OK mixer.

Above — The spectral output of a Mini Circuits Level 7 diode ring mixer for comparison. Conversion loss = ~ 6 dB at 4 MHz. Beautiful suppression of the LO and RF input signals. In my home brew diode rings, I usually get only about 35 - 40 dB RF and LO suppression due to mismatches in my diodes + transformers, and from layout asymmetry.

Update April 2, 2023 - - Discrete BJT mixer - -

I developed a very stable Gilbert cell mixer that uses no transformers in March 2023. I've run it from 2 MHz up to ~120 MHz with no VHF-UHF parasitic oscillations.

Above — An avionics band (119.6 MHz RF test frequency) mixer. Conversion gain = 10.1 dB. Despite 0 transformers, the LO was 22.9 dB down from the IF output conversion gain -- and the RF was 25 dB down from the IF conversion gain.

The input LO and RF are well defined at VHF and = 50 Ω. The output impedance is low and easily matched to 50 ohm input devices with a resistor or pi match. The Q4 collector resistor at 1.5K gave the best conversion gain, but this value may go as low as 1K Ω.  

Above — The IF output at 10.7 MHz. I used the BC547 CTA transistor for the emitter coupled pairs. This transistor consistently gives outstanding balance despite not matching my differential transistor pairs.

Above — My experimenters Gilbert cell mixer showing the variables such as capacitor choice versus frequency, setting up the 2 voltage divider bias networks, choosing mixer current & emitter degeneration to affect the input intercept. The BC547C specifies an fT of 300.   Thanks.

Above —  Yet another experimenters circuit for HF.

References

[1] B. Gilbert, “A precise four-quadrant multiplier with sub nanosecond response,” IEEE Journal of Solid State Circuits, Vol. 3, No. 4, December 1968, pp. 365-373.

[2] Syu, J.-S., Meng, C., & Wang, C.-L. (2013). A 2.4-GHz Low-Flicker-Noise CMOS Sub-Harmonic Receiver. IEEE Transactions on Circuits & Systems. Part I: Regular Papers, 60(2), 437–447