Combining Inputs and Offsetting by Separate Grounds

Greetings,

I'm not really sure about the subject line if it's right or not, but
it's basically what I'm looking to do.

I posted just yesterday a question about a circuit which was answered
very well by one T. Wescott. It turns out I simplified the problem too
much and a better representation is as follows.

Given inputs (P0, P, Q0, Q, R0, R)

P0 <> GND
P > P0
Q0 <> GND
Q > Q0
R0 <> GND
R > R0

And constants (A, B, C)

A constant < 1
B constant < 1
C constant < 1

Desire these outputs:

P* = A(P - P0) + B(Q - Q0) + C(R - R0) + P0
Q* = A(P - P0) + B(Q - Q0) + C(R - R0) + Q0
R* = A(P - P0) + B(Q - Q0) + C(R - R0) + R0

Note that the operation is the same other than adding a different
offset for each output.

Is there a simple solution for this? (e.g. just resistors)? Is there a
systematic way to scale up to more and more inputs and constants? e.g.
S0/S/D, T0/T/E, etc.

Any references on-line or otherwise are welcome. Any searches I do
bring up operational amplifiers which might be overkill for this kind
of application. And any searches I do regarding resistor circuits
don't seem to go beyond elementary introductions.

Thank you for reading.

Regards,

YR

 

[Jasen Betts]

On 2009-05-06, yiminrong@yahoo.ca <yiminrong@yahoo.ca> wrote:

Greetings,

I'm not really sure about the subject line if it's right or not, but
it's basically what I'm looking to do.

I posted just yesterday a question about a circuit which was answered
very well by one T. Wescott. It turns out I simplified the problem too
much and a better representation is as follows.

Given inputs (P0, P, Q0, Q, R0, R)

P0 <> GND
P > P0
Q0 <> GND
Q > Q0
R0 <> GND
R > R0

And constants (A, B, C)

A constant < 1
B constant < 1
C constant < 1

Desire these outputs:

P* = A(P - P0) + B(Q - Q0) + C(R - R0) + P0
Q* = A(P - P0) + B(Q - Q0) + C(R - R0) + Q0
R* = A(P - P0) + B(Q - Q0) + C(R - R0) + R0

Note that the operation is the same other than adding a different
offset for each output.

Is there a simple solution for this? (e.g. just resistors)?

no. consider the case where A=B=C=0.99

if you put the put P0,Q0, and R0 near ground and the the same
input signal on PQR you end up needing a gain of 2.97

and you can't get amplification from just resistors.

 

[whit3rd]

On May 6, 10:24 am, yiminr...@yahoo.ca wrote:

Greetings,


Given inputs (P0, P, Q0, Q, R0, R)

P0 <> GND
P > P0
Q0 <> GND
Q > Q0
R0 <> GND
R > R0

And constants (A, B, C)

Desire these outputs:

P* = A(P - P0) + B(Q - Q0) + C(R - R0) + P0
Q* = A(P - P0) + B(Q - Q0) + C(R - R0) + Q0
R* = A(P - P0) + B(Q - Q0) + C(R - R0) + R0

Note that the operation is the same other than adding a different
offset for each output.

Is there a simple solution for this? (e.g. just resistors)?

There are lots of solutions, and 'simple' isn't a good selection
criterion. With least parts, you can sum signals with resistors
onto two terminals of a transformer, and create your outputs by
summing multiple secondary windings of the transformer with
the inputs. That's one resistor for each term of the common
section, one transformer to perform the subtraction.

Is that clear? The transformer has two input terminals, call one (+)
and one (-); the secondary windings (you'll want three) will have
the (-) terminals wired respectively to P0, Q0, R0, so those
windings (+) terminals will produce the signals you describe.