tempco resistors

[Joachim Verghese]

On 2 May 1996, Christopher List wrote:

> If the temp-co of one transistor is cancelled by the other, where does this 
> extra temp-dependancy come in?

The collector current of a BJT (bipolar junction transistor) can be
described as

Ic = Is * exp(Vbe/Vt)

where Is is the reverse collector saturation current,
Vbe is the base-emitter voltage,
Vt is the "thermal voltage".

Both Is and Vt are heavily dependent upon temperature. The dependence
of Is can be cancelled by the use of a second transistor with similar
thermal behavior. This leaves the Vt term which affects the scaling
factor of the expo converter. This secondary temperature effect can
be reduced by multiplying the CV by a factor whose temperature coefficient
is opposite to that of the transistor. This is where the so-called tempco
resistor comes in useful.

> Also, if the transistor pair is driving an OTA to control the frequency, 
> doesn't the transconductance of the OTA have a temp-co? Does this affect the 
> ocillator (or filter) frequency?

Yes, it does. The Vt term is also present in the transfer function of
standard current controlled OTAs. The gain cells of Doug Curtis' (CEM)
filters were temperature compensated, but they were different in other
ways too. In the CEMs, the logartihm of the input signal is overlayed upon
the control voltage, and then applied to one BE junction of a differential
transistor pair. This way, the linear to exponential conversion takes place
in the gain cell itself.

-joachim