On 4/5/2014 6:26 AM, josephkk wrote:
> On Fri, 04 Apr 2014 10:45:21 -0400, Phil Hobbs
> <
pcdhSpamM...@electrooptical.net> wrote:
>
>> On 04/04/2014 09:04 AM, George Herold wrote:
>>> On Thursday, April 3, 2014 2:21:45 PM UTC-4, Tim Wescott wrote:
>>>> On Wed, 02 Apr 2014 17:26:21 -0700, RobertMacy wrote:
>>>>
>>> <snip>
>>>>
>>>> For "very linear" the diode-ring mixers (and, if you really want to
>>>> work at it, FET-ring mixers) have been recognized to be superior to
>>>> Gilbert cell mixers for years and years. I doubt that has changed,
>>>> although knowing whether a diode ring is superior to a FET ring is
>>>> beyond my pay scale at the moment.
>>
>>> Tim, do you have any idea why that is. "In theory" I would think the
>>> Gilbert cell would be better, 'cause it doesn't have all the odd
>>> harmonics that the switchers have. In practice I can imagine that
>>> switching is much easier than multiplying.
>>>
>>> George H.
>>
>> I don't think it's the current steering (upper) stage of the Gilbert
>> cell that's the problem--those devices are almost always ON or OFF.
>
> Not at all. They are operating in the linear portion of the tanh(x)
> curve. They could not do the job at all if they were bouncing in and out
> of cutoff and saturation. They have to stay in the active region or
> create all kind of nasty non-linearities and harmonics.
A barefoot Gilbert cell is a sorta-kinda multiplier. To make a good
linear multiplier, you have to work quite a bit harder than that.
Gilbert cell frequency mixers are generally run with the lower stage
linear and the upper stage switching. The upper stage works very much
like a MOSFET- or diode-ring mixer. Switching mixers do give you
intermod products of the form M*f_RF + N*f_LO, but you have to deal with
that anyway, because even a 1%-accuracy multiplier only gives you ~40 dB
spurious suppression, which generally is far too little. You deal with
it by picking a good frequency plan and building good filters.
The crucial advantage of switching mixers is that they don't give you a
lot of intermodulation between different signals on the RF port, i.e.
they suppress spurs of the form M*f_RF1 + N*f_RF2. Lots of those wind
up in-band, so filtering doesn't help nearly as much as a nice strong mixer.
And nobody in his right mind lets any of the transistors saturate.
Saturation is slow and noisy, whereas cutoff is well-behaved. If you're
running the Gilbert cell at, say, 3 mA total, then when the lower stage
is in balance, each of the upper stage transistors switch back and forth
from 1.5 mA to cutoff.
>
> BTW for all the people recommending saturated switching mixing, this is
> always followed be methods to suppress the harmonics generated. Which
> would likely reduce the accuracy of the measurements compared to not
> generating them in the first place.
Sometimes, depending on what the input signal looks like. The first
mixer in a receiver has a difficult life. Once you're past the first IF
filter, life gets a lot calmer. In an instrument application, where you
control what's in the input, you can sometimes design around the
problem. But linear multipliers aren't that great, especially not quick
ones. It's a lot easier to get 0.1% accuracy using a nice fast
switching mixer than a Gilbert cell.
>>
>> The main issue is that the RF port drives a BJT diff pair that's in its
>> linear range, so that its output current goes as
>> tanh(e dV_BE/(2kT)), whereas in a diode mixer the RF port's load is the
>> input resistance of the first IF, plus the switch resistances. Diode
>> mixers work a lot better into a constant 50 ohms for this reason.
>>
>> (Using a diplexer instead of a reflective filter after the mixer is a
>> big win for linearity, and this is why.)
>>
>> A strong interfering signal will drive the RF diff pair of the Gilbert
>> cell nonlinear just the way it does an ordinary BJT amplifier. Running
>> the diff pair as a current mirror, as in the LM13700 OTA, nominally
>> turns the tanh characteristic back into a linear one, but that trick
>> isn't often used at RF, I don't think.
>
>
> Really? There are plenty of Gilbert cell multipliers that stay well
> balanced from DC to past 100 MHz. The Gilbert cell is all about the
> tanh(x) properties of differential pairs. That is the basis of how it
> works.
Of course it is. It just isn't linear _enough_, when there are strong
interfering signals present. The Maclaurin series for tanh is
tanh(x) = x - (1/3) x**3 + (2/15) x**5 ....
For BJT pairs, delta I_C = I_tail * tanh(delta V_BE*e/(2kT)), so the
scale factor is about 50 mV.
The third order term reaches 1% of the desired signal when the input
amplitude gets up to
50 mV * sqrt(3/100) ~ 9 mV.
A properly designed linear multiplier does quite a bit better than this.
The diode trick that I posted is one of the simplest ways of patching
up the tanh characteristic, but there are lots of improvements you could
add, such as cascoding the lower stage. In a vanilla Gilbert cell with
sinusoidal LO, the lower stage collectors bounce up and down at twice
the LO frequency, which is another source of nonlinearity.
For receivers, there are other things that might be useful:
It would be sort of interesting to try replacing the lower stage of the
Gilbert cell with a center-tapped transformer secondary.
In a MOSFET bridge, it might be better to give each of the FETs its own
LO winding, connected G-S as in HV SMPSes. Driving the gates in pairs
gets rid of the even order distortion terms but not the odd order ones,
whereas separate gate drive should pretty well get rid of both.
Cheers
Phil Hobbs