^^^^^^^^^^
A small quibble, because this bit of Bad Info keeps popping up. A perfect mixer is a bilinear device: the IF output is linear in both the LO and RF signals. If you put some DC in the LO port, the RF->IF path satisfies all the requirements for a linear, time invariant network.
As you say, the image exists even with a perfectly linear multiplier, because of the identity
2 sin A sin B = cos(a-b)-cos(a+b).Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
I don't think a physical realisation exists at VHF or higher? Maybe for *very* small signals.
It's not really relevant what's possible under 1MHz, LM13700 etc.
Clifford Heath.
It's not challenging, but for those of us who chose our modulations, it's interesting. It's as relevant as we choose to make it.
Sorry. My comment on relevance was in the context of upsidedown's "SA as well as general coverage receivers and scanners". Not too many of those care about
Now I understand your negative attitude towards SDR, if you use that article as a reference :-)
Those dongle DVB-T chips are mainly intended for upper-VHF/lower-UHF applications in which noise figures are critical, but the signal levels are usually not too bad. Using it down to HF and lower (directly or via an upconverter) will cause signal handling problems.
The only 8 bit ADC forces the use of some preamplifier with AGC in front of the ADC. The small dongle size doesn't allow much front end selectivity.
I am thinking more about SDRs with Tayloe mixer/detector followed by
16-24 bit "audio" ADCs. The Tayloe mixer/detector consists of four S&H units each fed with 90 degree phase shift from each other, two differential amplifier generating I and Q signals. These are typically implemented with a 1 of 4 bus switch and a dual op-amp.The I and Q signals can then be processed in analog or digital domain. If processing is done in digital domain, the I and Q channel phase shift and amplitude variations can be quite well be compensated to give goo opposite sideband suppression.
You still haven't told me anything I didn't already know.
A Gilbert cell made from 80 GHz SiGe:C bipolars should be able to do linear multiplication up to ~10 GHz. With unmatched transistors it would take a bit of tweaking, but they cost 25 cents each in small quantity.
Normally
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
Linear in what signal levels? Don't you have to stay under a couple of mV? It's not normal to drive a Gilbert cell that way.
I have some HFA3101's coming, which are only 10GHz Ft, but then I only really care about mixing
A real Gilbert cell is a current-mode device--the inputs drive current mirrors (what the LM13700 data sheet calls "input diodes"). That ideally gets rid of the tanh nonlinearity.
A lot of the time hard-switching is better because diode-bridge and poorly-designed Gilbert-style mixers generate most of their IMD during the transitions and because hard switching gets rid of the AM noise of the LO.
It would be fun to build a BFP840 Gilbert cell and see how it worked. Based on their Spice models they should have excellent log conformity.
Cheers
Phil Hobbs
Ideally... not sure if you're right. No-one actually builds an RF multiplier that's linear in both ports. Maybe linear in the RF port, but not in the LO port. The best I know of is the AD734x, which at $26 is linear to 10MHz.
For zero-IF conversion, a linear device would prevent the need for RF filters, because you wouldn't need to be demodulating spectrum at 3LO, 5LO, etc.
So if you know how to do it at 10GHz, you should sell the idea to Analog Devices and retire in your choice of castle.
In other words, show us the LTSpice simulation!
Clifford Heath.
The math is not at all difficult--it's just Ebers-Moll. (You were the one who brought up (the "perfect mixer", not I.)
That's a marketing decision, not a technical one. Pals of mine at IBM were building single-chip 65-GHz transceivers over a decade ago.
Cheers
Phil Hobbs
Technically, it would be noisier compared to a switching mixer, and making the LO port linear would make the other (RF) port less linear. Whether to bet that there is a market for noisy mixers with lousy IP3 is a marketing decision.
Also, it is just shifting the problem because it is not simple to generate a very clean sinusoidal LO signal that can be readily swept over several octaves. If you are averse to banks of switchable filters then a DDS is probably the best (or least-worst) choice but they suffer from spurs (admittedly less so these days). You might be better off ditching your both-ports-linear mixer, and instead build a DDS with a multiplying DAC, (configured to multiply the digital value by the RF signal).
If the highest required RF frequency is not too high (maybe 1/128 of the switching speed of a nice fast mixer), then a direct-conversion receiver with good rejection of the odd harmonics of the LO could be constructed by another method: A digital sigma-delta modulator would be used to produce a bitstream at some high bit rate, where this bitstream is a noise shaped approximation of a much lower frequency sinusoidal LO signal, much like the bitstream used by a 1-bit audio DAC of a CD player that is playing a CD of a sine wave. The LO port of a fast switching mixer would be driven by this bitstream, making the RF port of the mixer sensitive at the frequency of the sinusoid, but not sensitive at the low harmonics of the sinusoid frequency, since those low harmonic frequencies would be absent from the LO bitstream. Of course the bitstream contains a lot of shaped noise at much higher frequencies, and the RF input of the mixer would be sensitive to these frequencies. Therefore, to prevent the whole radio from exhibiting these spurious responses, a low-pass filter would be required before the mixer (but only one, not banks of them), and to get the best noise figure, enough gain would have to be put before this filter so that the RF signal at the wanted input frequency is comfortably stronger than the mixer's RF port's own internal noise at the frequency range of the LO's shaped noise. One advantage of this technique is that for an I-Q pair of mixers, excellent LO quadrature could be achieved, since the sine and cosine LO bitstreams are generated digitally.
Ground control to Major Chris. ;) I'm not expressing any opinion about the relative merits of linear and switching mixers. I usually use fast CMOS muxes myself, and have for years. They're duck soup. For protos I often use Mini Circuits Level diode mixers with +17 dBm LOs.
I can see the usefulness of good linear multipliers, and there's no reason a multiplier has to be noisier than a switching mixer. Analogue multiplier chips usually have ridiculous voltage dividers in front of them so as to change their input range to volts from millivolts. That's going to hurt the NF for sure, but it's not a fundamental feature of BJTs. The SiGe:C ones I like are very quiet--Rbb' of a couple of ohms, Ree' way under an ohm, betas getting on for a thousand, f_T ~ 45 GHz (BFP640). That's quieter than your average Schottky mixer diode.
The main noise issues are image noise (which gets downconverted into the IF if you don't filter it out ahead of time) and the AM noise of the LO.
My interest was mainly in correcting the Bad Info that a mixer is intrinsically a nonlinear device, which it need not be. That's periodically repeated round here, and in the past has led to some fairly serious confusion.
In my first reply to Cliff, I described it as "a small quibble", after all.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
Ok fair enough.
Ok, perhaps in theory, but I can't yet think of any way to build a linear multiplier that would be as quiet as a good switching mixer (when used as a direct conversion receiver). Perhaps it would be possible but I think that it would have to be not based on a BJT Gilbert cell, as in those, (with a noiseless RF signal) when the LO transistors are balanced, the gain to the output from the RF signal is near zero, but the noise is bigger then when the LO port is strongly unbalanced.
If you can think of a suitable topology, that would be very interesting to explore. I wonder whether the LO signal could be used to drive the gates of MOS devices that are biased in the triode region - their conductivity is fairly linear with the gate voltage, and they pretty much just have Johnson noise then (in the absence of DC channel current or a strong RF-port signal) but I have not fully explored how to configure them into a mixer. Also being in the triode region implies a small RF-port signal, so noise crops up again. I did once implement a variable gain stage using BJT cascode devices with triode region NMOS devices as the emitter resistors. The signal went to the MOS gates and the gain was varied by biasing the base of the BJT cascodes. Perhaps that could be turned into a mixer, but I doubt it would be anywhere near as good as a MOS switching mixer.
I think that at least for the LO port, that is pretty much unavoidable. If the interesting ("linear") range of LO signals is that in which the current is shared between the two transistors in a pair but not "hard switched", then the voltage between the bases of the pair will only be a small multiple of kT/q, so the Johnson noise of the base resistance (amongst other things) will be hard to ignore.
Sure, e.g. you can make quiet, hard-switched mixers with BJTs ;-) but I think it might be a fundamental feature of translinear operation.
Yes, ok, but pretty much all available *good* mixers are non-linear on one port (where "good" means low-noise and having at least one port that is quite linear, with stable gain).
Doesn't make a difference--the active device in the LO has the same problem, and its phase noise doesn't go away. Plus the Johnson noise of Rds(on) gets downconverted to the IF anyway, so it's pretty much a wash if the bipolars are quiet.
No, it's the noise of the active devices. Quiet ones are as quiet as diodes or muxes. Muxes have Johnson noise just like resistors, so if the Rbb' and Ree' of the transistor are lower than Rds(on), the BJT is quieter. (There's also base current shot noise to worry about, but with betas near 1000, the SiGe:C devices don't have much of a problem there.)
Well, some of us design stuff. (Just kidding.) Building a good mixer from scratch isn't very hard--the issues have to do with balance, but in a BJT circuit that's easily trimmed out. It all depends on whether it's worth the hassle, which, I agree, it usually isn't.
I used to do satcom stuff in a previous life, but It's been a long time since I've designed a communications receiver, but I do a fair amount of RF signal processing in electro-optical instruments, most recently in an
8-GHz coherent lidar and a two-axis acousto-optically scanned interferometric laser microscope.The challenges are somewhat different in my biz--very strong interfering signals are rare, but the linearity requirements are typically very strict--much better that the 8-bittish accuracy of communication-type SDRs or oscilloscopes.
I did the laser microscope proto really old school. The challenge was that there were two octave-bandwidth VHF control signals, one for each axis of the scan. The signal from the detector was at 2(f_x + f_y), so in order to get that to some nice IF where there were good filters available for cheap (10.7 MHz), I needed to generate a quiet LO at 2(f_x
This was a proof of concept, and I was in a hurry, which is why I did it old school, the way I would have circa 1982. It had offset PLLs and frequency doublers and stuff. Tuning both f_x and f_y independently over an octave band, that resulted in a forest of spurs, for sure. However, a 1:1 PLL on the output cleaned it right up, and it worked great. Unfortunately, due to the 2015 chip-making downturn, Intel pulled the funding plug from my customer, so it never got commercialized. (After the proof of concept, the real version was going to use dual DDSes with a carefully chosen frequency plan to minimize in-band DDS spurs, but I never got to build it. A pity--maybe it'll come back from the dead one of these days. Projects sometimes do.)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
I don't understand this. I was talking about a differential pair of BJTs where the RF signal is applied as a current to the tail (the emitters) and the bases are driven by a LO signal. If the bases are driven with a large amplitude square wave as in a hard-switched mixer, then (other than the small base current noise), the transistors only contribute noise to the output at the collectors for a very brief period during which the LO signals are switching and both collector currents are significant. The rest of the time, the collector current of the transistor that is "on" has pretty much the noise of the emitter current (apart from the base current noise contribution which is small). If instead, the pair is used as part of a multiplier, then all of the time both transistors are conducting significant current, and all of the time, the output will be affected by noise from the transistors, e.g. the Johnson noise of the base resistance amongst other things. I did not discuss phase noise, as I think both sorts of mixer are similarly affected by this.
Sorry, what is? I was saying that using a differential pair of BJTs in a translinear circuit e.g. an analog multiplier, makes the BJTs contribute more noise than when the differential pair is used as a switch, to steer the emitter current entirely to one collector or the other.
Yes I accept that BJTs can be used in quiet mixers. My point was that when they are configured in an analogue multiplier rather than as a switch, the output noise tends to be greater.
I think designing one that is very linear on both LO and RF input ports, and quiet, would be quite a challenge. When I said that pretty much all available *good* mixers are non-linear on the LO port, I didn't mean that a discrete mixer would be better that the available ICs, I just meant that as far as I can tell, nobody knows how to design one that is linear on both ports and quiet, or if somebody does know, they are keeping it a good secret. I don't think that it is impossible so I'd be interested to hear ideas about how one might go about it.
As I understood it, this branch of this thread was about whether it is feasible to build a mixer that is linear on both RF and LO input ports, i.e. an analog multiplier, without making it worse in other respects (such as noise, and linearity on the RF port) than a hard-switching mixer. Maybe I'm barking up the wrong thread.
Sure. But with a 6-ohm Rbb' and effectively zero Ree' (see Spice model below), the transistor noise is way below the Johnson noise.
Additive noise produces both phase and amplitude fluctuations:
= 1/sqrt(2 CNR) and
= 1/sqrt(2 CNR).
MUXes have at least as much noise as good transistors, just from their ON resistance.
Gilbert cells and other translinear things do tend to multiply shot noise, which to me is their major drawback. An un-degenerated current mirror produces sqrt(2) times full shot noise in its output. On the other hand with emitter resistances that low, the log conformity is good enough to run them pretty hot. In a discrete design, you can run the input device of the current mirror at higher current than the pass device.
Then the main noise source is partition noise--if you feed a BJT diff pair a tail current with full shot noise, ideally both collector currents have full shot noise irrespective of Delta V_BE. Thus at a
50:50 split ratio, each transistor contributes 1/sqrt(2) of full shot noise to its collector circuit. It drops at nonzero Delta V_BE: in the limit of large splitting ratios, the low-current side has full shot noise and the high current side has none. You can reduce the effect by using diode-connected transistors for the degeneration, but you only win linearly so it's not that much help except in laser noise cancellers.It's an interesting problem, I agree. Maybe one of these times I'll have a whack at it.
Here's the BFP640 Spice model for your delectation:
.MODEL BFP640FESD_DIE NPN(
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
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