AW: Four multipliers for frequency shift

[Kimmo Koli]

On Fri, 15 Nov 1996, Haible_Juergen#Tel2743 wrote:

> > why not use two LM13700 to make four four-quadrant multipliers.
> > If the linearisation diodes are used then the four-quadrant operation
> > works independent of temperature unlike the 3080 multiplier.
> 
> Are you sure ?? Fully temperature compensated ?

Well, anyway much better than a 3080 four-quadrant multiplier which has some
level of carrier suppression at one temperature only. A one OTA LM13700
four-quadrant multiplier with linearization diodes has smaller temperature
dependency. The voltage accross the linearizing diodes (0.7V) and the bias 
current input voltage (V- + 1.4V) add temperature dependencies. But if we
use current sources to these nodes, temperature independent operation should
be the result (at least in theory...). By generating Id and Iabc with 
resistors from the positive supply should do nicely also:
    Id = (Vcc - 0.7V) / R1
  Iabc = (2*Vcc - 1.4V) / R2 = 2 (Vcc - 0.7V) / R2
And the OTA-gain should be proportional to Iabc/Id only.

Of cource the circuit has a lot of other nonidealities that were not in these
equations. Therefore using a two OTA multiplier I proposed, most problems are
cancelled by using an on-chip replica circuit. And this is done without 
trimming (exept for offset voltages). 

> > If the linearization diodes are used the circuit is similar to 
> > "linearized"
> > Gilbert-cell with some extra current-mirror in the output.
> 
> It's not the same! The linearisation only works with *current* sources
> to the diodes. The usual voltage-source + resistor-in-kOhms-range
> is a rather bad approximation for a current source.

Yes, you are right that current sources are needed for best performance.
But you can supply current also to the linearization diodes of LM13700.
But the benefit from the lineriazing diodes are small anyway, they only
enable a bit larger input voltage swing.

> > Benefit from this circuit: a four quadrant multiplier without trimming.
> 
> I don't believe that. One word: Offset voltages! Even these expensive
> multipliers from Analog Devices need trimmers.
> 
I thought that nobody would believe that the circuit really compensates 
offset voltages. Offsets are totally random so no replica circuit can 
compensate for them. But the temperature drift is fully compensated (to 
the level of on-chip mathing), even the effects of the vbe's of the Iabc 
input are compensated for. 
 
> > I build a frequency doubler some five years ago like that and it worked 
> fine.
> 
> Without trimming? I bet you had very bad carrier suppression then.
> Which might be no problem for a frequency doubler, but is crucial
> in a frequency shifter.
 
In a frequency doubler good carrier suppression is not needed because 
both multiplier inputs are the same anyway.

Thats all,
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   Kimmo Koli                         Helsinki University of Technology 
   kimmo at ecdl.hut.fi                  Electronic Circuit Design Laboratory
   http://www.ecdl.hut.fi/~kimmo      Otakaari 5 A 
   Tel:  +358 9 451 2273              FIN-02150 Espoo
   Fax:  +358 9 451 2269              Finland 
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