Fri Jan 7 22:41:57 EST 2011

Voltage controlled envelope using exp converter

Using the exp controlled sawtooth/ramp circuit we could use larger
integrator cap values to construct larger slope ramps and feed the
ouput to yet another exp converter.  If biasing and impedance do not
give problems this gives a very simple exponential decay with
exponentially controlled time constants.

While the "free" exponential decay that comes from an RC network seems
much simpler, a voltage or current controlled resistor that works at
DC isn't exactly cheap to build[1].

This circuit could also serve as an exponential pulse oscillator which
decays into a saw by varying the amplitude. (??)

                         --o-----------------o-- Vcc
                           |                 |
                           |                 >
                         ===== C2            > R3
                           |       R2        >
TRIG/   o------------------o---/\/\/\/\--o   |
DISCH                      |             |   o--o Vout
            R1             /             |   |
PWM     o---/\/\/\/--o---|/  Q1          | | / 
                     |   |\              o-|/  Q2
                     |     V               |\
                C1 =====   |                 V
                     |     |                 |
                     |     |                 |
                   --o-----o-----------------o-- GND

Instead of R3, the output could also be a current into an opamp
virtual ground biased around 1/2 Vcc.

As far as careful design goes, this circuit is horrible.  But can it
be made to work with proper driving and some voltage feedback from


  R2 is necessary for limiting Q2 base current when DISCH is set to
  Vcc, driving Q2 into deep saturation.


  The useful range over C2 is quite small.  For a 100x envelope range
  it's about 100mV.  The main problem however is to initialize the C2
  voltage to the proper bias before starting the linear charge ramp.

In order to solve the biasing problem of Q2, the following
re-arrangement will probably be better.

                         --o--------------o-- Vcc
                           |              |
                           |              >
                         ===== C2         > R3
              R2           |              >
TRIG/   o---/\/\/\/--------o------o       |
DISCH                      |      |       o--o Vout
              R1           /      |       |
PWM     o---/\/\/\/--o---|/  Q1   |       / 
                     |   |\       o-----|/  Q2
                     |     V            |\
                C1 =====   |              V
                     |     |              |
                     |     |              |
                   --o-----o--------------o-- GND

Here the voltage at C2 and base of Q2 can't go over V_BE.  The
envelope swing will be maximum, only limited by the saturation voltage
of Q2.  Releasing the DISCH will start the ramp over C2 which will
first take Q2 out of saturation (a small envelope delay) and then will
start decreasing the current through R3 creating an exponential curve.

When Q1 reaches saturation due to C2 charging, the voltage over Q2
base will be small enough to make the current through R3 negligible.
I.e. it's past the useful part of the curve.

The only thing to be careful about is the base current of Q2.  Once
DISCH is off, it will be provided by C2, leading to a faster discharge
of C2 in the beginning of the ramp.  However, R3 can be relatively
large, which makes the bias current small.

There seems to be a problem with size of C2 though: it needs to be
large to provide Q2 bias current, and R2 needs to be relatively large
to limit Q2 saturation current, so the product is large, which makes
discharging C2 a time consuming operation.

Is the following reasoning correct?

   R2 needs to be relatively small to keep the R2C2 time constant
   small because C2 will be relatively large.  This means Q2 will be
   deeply saturated.  This allows for some wiggle room to make the
   circuit not depend too much on h_fe of Q2.  This saturation current
   will be high compared to the current through Q1, which will make C2
   drop voltage fast.  However, in order for this initial relaxation
   not to show in Vout, the base current of Q2 needs to become small
   in relation to the current through Q1 _before_ Q2 leaves
   saturation.  Then the ramping voltage will bring Q2 out of
   saturation, starting the exponential decay with a slight delay.
   This delay needs to be small compared to the rise time of Vout.
   That might be a problem.

Conclusion: Q2 biasing seems to be too sensitive to component
parameters, so it might be best to use feedback for setting the bias
point.  Something like this:

                         --o-----------------o-- Vcc
                           |                 |
                           |                 >
                         ===== C2            > R3
                           |                 >
              R2           |                 |
                           |            o----o--o V_out
DISCH                      |            |    |
TRIG/   o---/\/\/\/--------o------o     >    |
                           |      |     > R4 |
              R1           /      |     >    |
PWM     o---/\/\/\/--o---|/  Q1   |     |    / 
                     |   |\       o-----o--|/  Q2
                     |     V               |\
                C1 =====   |                 V
                     |     |                 |
                     |     |                 |
                   --o-----o-----------------o-- GND

With DISCH and Q1 current source disconnected, the transistor will be
in forward active mode, and the V_out bias point will depend on the
current gain b as (1 + b/b_0) where b_0 is the nominal current gain.
V_out nominal could be set to 1/2 Vcc, allowing for about 50% current
gain mismatch.

It seems that it really isn't straightforward.

[1] http://www.avtechpulse.com/papers/vres/