On 07/10/2017 10:11 AM, Chris Jones wrote:
> On 07/07/2017 01:57, Phil Hobbs wrote:
>> On 07/06/2017 10:14 AM, Chris Jones wrote:
>>> On 06/07/2017 23:42, Phil Hobbs wrote:
>>>> On 07/06/2017 08:16 AM, Chris Jones wrote:
>>>>> On 06/07/2017 21:22, pcdhobbs@gmail.com wrote:
>>>>>>> Ideally... not sure if you're right.
>>>>>> The math is not at all difficult--it's just Ebers-Moll. (You were the
>>>>>> one who brought up (the "perfect mixer", not I.)
>>>>>>
>>>>>>> No-one actually builds an RF multiplier that's linear in both ports.
>>>>>>
>>>>>> That's a marketing decision, not a technical one.
>>>>>
>>>>> 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).
>>>>
>>>> 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.
>>> Ok fair enough.
>>>
>>>> I can see the usefulness of good linear multipliers, and there's no
>>>> reason a multiplier has to be noisier than a switching mixer.
>>> 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.
>>>
>>>> Analogue multiplier chips usually have ridiculous voltage dividers in
>>>> front of them so as to change their input range to volts from
>>>> millivolts.
>>> 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.
>>
>> 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.
> 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.
Sure. But with a 6-ohm Rbb' and effectively zero Ree' (see Spice model
below), the transistor noise is way below the Johnson noise.
> 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.
Additive noise produces both phase and amplitude fluctuations:
<delta Phi> = 1/sqrt(2 CNR) and
<(delta A)/A> = 1/sqrt(2 CNR).
>
>>
>>> [for context]...the Johnson noise of the base resistance
>>> (amongst other things) will be hard to ignore.
>>>> That's going to hurt the NF for sure, but it's not a fundamental
>>>> feature of BJTs.
>>> Sure, e.g. you can make quiet, hard-switched mixers with BJTs ;-) but I
>>> think it might be a fundamental feature of translinear operation.
>>
>> No, it's the noise of the active devices.
> 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.
MUXes have at least as much noise as good transistors, just from their
ON resistance.
>
>> 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.)
> 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.
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.
>
>>
>>>
>>>> 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.
>>
>>> 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).
>>
>> 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 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.
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(
+ IS = 1.542E-015
+ BF = 642.6
+ NF = 1.014
+ VAF = 355.5
+ IKF = 0.1782
+ ISE = 3.98E-015
+ NE = 1.737
+ BR = 49.18
+ NR = 0.98
+ VAR = 1.378
+ IKR = 0.1924
+ ISC = 3.85E-015
+ NC = 1.5
+ RB = 6.00965
+ IRB = 9.099E-006
+ RBM = 1.74736
+ RE = 0.0142
+ RC = 4.54
+ XTB = -2.514
+ EG = 1.11
+ XTI = 0.808
+ CJE = 1.676E-013
+ VJE = 0.6804
+ MJE = 0.2508
+ TF = 1.836E-012
+ XTF = 2.279
+ VTF = 0.9972
+ ITF = 0.6365
+ PTF = 0.2896
+ CJC = 8.39234E-014
+ VJC = 0.5464
+ MJC = 0.3098
+ XCJC = 0.6466
+ TR = 1.489E-007
+ CJS = 2.15519E-013
+ MJS = 0.2426
+ VJS = 0.29
+ FC = 0.8156
+ KF = 123.5E-12
+ AF = 1.89)
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