RE(2): matched expo source / sink idea

[Haible Juergen]

Hi Terry,

I've never dug too deep into transistor parameters, so I try to rely on
comparison with the original 2 transistor circuit (consisting of Q1, Q3
and R3) for my argumentation.

The short form is that you're right about varying betas and base currents,
but I think it's not really important, and there is no more variation in the
proposed 4 transistor circuit than in the original 2 transitor circuit.

In detail:

	> The base/collector current ratio
	>(beta) is not a linear relationship, beta varies with the standing
	>collector current, collector voltage, temperature, etc.   The base
current
	>of Q1 is dependent on the beta of Q4.  Since beta can vary for
several
	>different reasons, I wouldn't want to depend on it to accurately
drive the
	>following transistors. 

Why would the current thru Q1 and Q4 be important at all ?
I think the whole exponential conversion is done with Q2 and Q3, and the
only two tasks for Q1 and Q4 are to provide a voltage shift that varies with
4mV/K,
and to provide this voltage with a low impedance. The absolute value of this
voltage,
or the value of the current thru these transistors, is not important at all,
as long
as it's in a range where the 2mV/K per transistor is valid with good
accuracy.
The two stages Q4 and Q1 are voltage-in / voltage-out, and the currents are
not
important as long as their effects cancels in regard to the voltage transfer
function.

I want to look at the currents, nevertheless.
The base currents of Q1 and Q4 are determined by the supply voltage,
by R3, and by the beta of Q1 - that's the major influences that determine
the
current to 99.5%, the remaining 0.5% being determined by voltage variations
across the BE paths of Q1 and Q4. The surprising result is that there is
practically
no other influence on the base current of Q1 in the 4-transistor-circuit
than in
the widely used 2-transistor-circuit ! Beta (of Q1) may be temperature
dependent,
but if that has any influence, it would deteriorate the behaviour of both,
the old
and the new circuits. Beta of Q4 does not have a 1st order effect on the
base
currents of Q1 and Q4 at all. The collector current of Q4 is a "don't care"
for the
output signal of the 1st stage, as long as it is in a reasonable range, and
stays
fairly constant - which it does.

But I have found a different drawback of the proposed circuit: It needs a
lower
driving impedance than the 2-transitor circuit, as the buffer operation of
Q1 is
sort of reversed by Q4. An opamp output might be needed to drive this
circuit,
rather than a simple resistor divider.

I couldn't resists to build the circuit last night. I had no time to make
any precise
measurements, but at least it works and doesn't do any strange things like
latching
up etc. This does not say anything about the usabillity as a precision expo
converter
for VCOs, of course. OTOH, now that I know that all transistors are smoothly

operating in "normal" regions (despite the stupid circuit), I have regained
some
confidence in my Spice simulations. Which showed a straight line in log
scale
from 5nA to 1mA.

Stupid circuit it is, nevertheless. Who would sacrifice the advantage of a
high
impedance input of the 2-trans circuit by "inverting" the emitter follower
operation ?!
So in practice, I would go for Osamu's version, or for your diode + load
resistor
version.

As for driving a transistor base from another one, isn't this also done in
some bipolar
opamps to achieve high input impedance ?

JH.




>  Also, transistors are designed and optimized so the
	>base current controls the collector current.  They are not
characterized
	>for use in the reverse direction, i.e., the emitter current
controlling the
	>base current.  This may adversely affect the exponential transfer
function.
	>
	>
	>Terry Michaels