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Design >> Mixed-Signal Design >> subtractor
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Message started by cktlife on Sep 14^th, 2007, 12:09pm

Title: subtractor
Post by cktlife on Sep 14^th, 2007, 12:09pm

Hi all,

I am trying to design a high speed voltage/current/charge subtractor without using opamp. One input is from DAC. Can any circuit do that?

Thanks,

Title: Re: subtractor
Post by carlgrace on Sep 19^th, 2007, 1:41pm

Try putting two simple amplifiers in parallel: A common-source stage loaded with a resistor and buffered by a source-follower is connected to one input. The output of this stage will be the output of the subtractor. Then another common source stage with the source terminal of the original source follower as a load will be connected to the second input. Assuming ideal components (in particular a source-follower gain of one) the gain of this circuit will be (we are applying the principle of superposition here):

Av = -(gm1Rload)Vin1 - (gm2/gm_sf)vin2

here gm1 is the gm of the first common-source device
Rload is the load resistor of the first common-source device
gm2 is the gm of the second common-source device
gm_sf is the gm of the source-follower device that buffers the output of the first common-source device and acts as the load for the second common-source device.

Title: Re: subtractor
Post by vivkr on Sep 20^th, 2007, 3:10am

Hi Carl,

Isn't your circuit just adding the 2 inputs. From your gain expression, I see that both inputs are combined and both are
inverted.

Perhaps, one needs to add an extra inverting stage (common-source) with the second input before passing it to the second
common-source stage whose load is the source of the source follower.

If the 2 common-source stages with resistive load have the same gain, and the gm of the source follower equals the gm of
the common-source transisor whose drain ties to the source, then one could get a subtraction of the 2 inputs.

Regards
Vivek

Title: Re: subtractor
Post by vivkr on Sep 20^th, 2007, 3:16am

Actually, the best solution might just be to use a differential pair for the subtraction but realize a gain of 1 in it (if you don't want gain >1 that is).

I assume of course that a diff. pair is acceptable when you speak of realizing this function without an opamp.

Several ways exist:

1. Use diff. pair with resistive loads but gmRl =1. You would need a diff.-single converter here.
2. Use diff. pair with current mirror load and set gm of load devices = input devices.
3. Use BJTs for both input and load devices and connect load in a diode-connected manner (gm automatically equal), again need a single-diff.

Surely, even more methods exist, limited by the imagination of the user.

Regards
Vivek

Title: Re: subtractor
Post by carlgrace on Sep 20^th, 2007, 6:13am

Vivek,

I think you right, you would need to invert one of the inputs. Not really a big deal I imagine. Sure you could use current domain techniques to implement the subtraction as well. Good ideas you had.

Carl

Title: Re: subtractor
Post by tosei on Sep 24^th, 2007, 7:29pm

If high speed is a must, among the ideas vivek proposed I would mainly go for the resistive load one, since it avoids using diode connected devices, which slows down the transient response of the circuit.

Another option would be to use a passive switched cap network (no opamps), where the subtraction is simply achieved by inverting the polarity of one of the sampling caps at the time the charge sharing is performed. In order words, two caps sampling Q1 and Q2 charge if connected in parallel (in the other clock phase) will average such charge ((Q1 +Q2) /2), while if they are connected in an "anti-parallel" way the subtraction is performed.

tosei

Title: Re: subtractor
Post by vivkr on Sep 24^th, 2007, 11:24pm

Hi Tosei,

Yes, capacitors could do it quite fast too. However, there are 2 problems with these:

1. Parasitic sensitivity will mean that the parallel and anti-parallel case are not the same, unless of course one uses 2 elements in parallel to realize each
unit cap, with top and bottom plates oriented differently for each unit cap. However, there is still parasitic sensitivity which will change the gain from 1
to something less.

2. Loading of the output by the next stage will cause a further error. If the load is a cap, then it translates to another gain error. If it is a resistive load, then
the situation is worse. One has distortion.

Regards
Vivek

Title: Re: subtractor
Post by cktlife on Sep 25^th, 2007, 7:55am

Hi,

Thanks for all. CS + source follower solution works for small signal subtraction. For large signal, the voltage difference is converted into current so a I-V converter is needed. The simplest one is diode connected MOS, taking its gate voltage as output. But it is nonlinear due to channel length modulation. Body effect can be removed by choosing appropriate mos. By sweeping linear input and DAC values, the output suppose to be a sawtooth shape. But zeros shift in y direction. Any idea to get rid of this or other better I-V converter.

Title: Re: subtractor
Post by tosei on Sep 25^th, 2007, 4:06pm

Hi vivek,

You are right concerning the parasitics affecting the gain when talking about the switched-caps option. Certainly this is more suitable when using an opamp so you can use the stray-insensitive arrangement

tosei.

Title: Re: subtractor
Post by cktlife on Oct 14^th, 2007, 7:06am

Hi vivkr,

Diff to single converter i know uses diff pair again. Any suggestion on simpler diff to single converter?

Thanks,