1/X circuit

[Donald Johnson]

Here's a circuit a found some years ago. I haven't built it,
but it seems simple enough. It's like Rene Schmitz suggested:

> Logarithmic V/V convertor, invertor, expo V/V convertor.
> Since exp(-log(x)) = 1/x. It will work only for positive input. 
> I think it won't need a tempco resistor, since the log tempco cancels
> the exps tempco.

Good luck.
don.

Tony Allgood wrote:
>>Voltage controlled symmetry... I think 1/x is not a good way, because
>>of exessive error.
>
>You may be right Martin, but I'm planning to do it for a LFO, so tight
>frequency is not a real issue. In fact, by using a standard expo the
>frequency only droops by about a factor of 2 for 80% m/s output. Might
>just be good enough, to see if the idea is worth persuing.
>
>>Don Tillman came up with a good idea how to do this via exponential
>>functions. Recommended..
>
>Don are you there... I missed this one. Is it on the archive yet?
>
>And I've just noticed Paul's MOTM LFO does have a shape control. Any
>hints Paul? Or does your work in a different way.
>
>BTW- e-mail probs are over; Freeserve my ISP were having a little
>problem installing some new thingummies.
>
>All the best,
>
>Tony

p.s. I've attached a gif and the original text
    (with poorly formatted formulae :( ).
  .. Donald Johnson               | MDSI = Mobile Data Solutions ..
 ... Software Development Manager | 10271 Shellbridge Way        ...
.... (604) 207-6481 [voice]       | Richmond, B.C.               ....
.... (604) 207-6060 [fascimile]   | Canada                       ....
 ... (604) 207-6000 [reception]   | V6X 2W8                      ...
  .. djohnson at mdsi.bc.ca          | http://www.mdsi-advantex.com ..
-------------- next part --------------
The following section of this message contains a file attachment
prepared for transmission using the Internet MIME message format.
If you are using Pegasus Mail, or any another MIME-compliant system,
you should be able to save it or view it from within your mailer.
If you cannot, please ask your system administrator for assistance.

   ---- File information -----------
     File:  1_x.gif
     Date:  27 Jan 2000, 9:38
     Size:  5975 bytes.
     Type:  GIF-image
-------------- next part --------------
A non-text attachment was scrubbed...
Name: 1_x.gif
Type: image/gif
Size: 5975 bytes
Desc: not available
URL: <http://synth-diy.org/pipermail/synth-diy/attachments/20000127/ed1e679e/attachment.gif>
-------------- next part --------------
---------------------------------------------------------------------------

Transistor array cuts cost of algebraic inversion

by Pavel Ghelfan
M.G. Electronics Ltd., Rehovot, Israel

---------------------------------------------------------------------------

Monolithic operators for algebraic inversion are convenient, but a reliable
algebraic inverter can be built quite simply and at less cost from an
integrated five-transistor array and two operational amplifiers. The circuit
first converst the the input signal to a logarithmic equivalent and then
takes the antilog of this.

The output voltage (VL) of amplifier A1 is a logarithmic function of the
input current (IIN) and the current (IR) that the transistor arrays sinks
as pin 13:
                                                     2
        2kT    ( IR  )    kT   ( IIN )    kT   (   IR    )
  VL = ----- ln(-----) - --- ln(-----) = --- ln(---------)
         q     ( IES )    q    ( IES )    q    ( IIN IES )

where IES is the emitter saturation current (with collector shorted to base)
of the array's transistors, k is Boltzman's constant, q is the charge of an
electron, and T is the absolute temperature. The antilogarithmic operation
is performed by amplifier A2. The circuit's output signal can be expressed
as:
                                     2
                   (     q  )      IR
  VOUT = IES R1 exp( VL --- ) = --------
                   (     kT )    R1 IIN

Trimming the value of the constant current IR will adjust the numerator of
this equation so that the output voltage of the circuit is brought to the
desired value and kept there.

The inversion operator maintains good stability over a 50 degree C
temperature range, as well as over three decades of signal amplitude
variation. Its amplitude range can be significantly broadened by using
low-bias-current operational amplifiers.

---------------------------------------------------------------------------

Op amps: National LM308
R1 : 20K