Hi Mark,

Try modeling the op-amp as a voltage source whose output is a large
number (make it a variable G or A) times the difference between the
non-inverting and inverting inputs. The exact value of G should not
change your answer much. If you want to be even more accurate, you
could model it as a voltage source whose output is as above PLUS a
smaller number (G/Q, where Q would be the common mode rejection ratio,
or perhaps a factor of 1000 or 10000) times the sum of the two inputs.

Another non-ideality which will come into play is the offset voltage
of the op-amp. To add this in, use the above model but also add in a
constant to the output (this constant should be a few millivolts times
G). G will typically be around 1 million.

Let's say that the op-amp has an offset voltage of 1 millivolt. Then
V+ and V- will sit 1 millivolt apart. This means that the current
0.001/Ra has to come from the feedback network. It will come from the
100k resistor (at least up until the opamp saturates) since the
voltage on either side of the 10k resistor is fixed. This means that
the output voltage will have an error of 100k/Ra times 0.001 or
100/Ra. This will be 1 volt for a 100 ohm resistor.

If the op-amp is not a cmos type and has significant input bias
current, then this will add to the error involved.

Sean


On 8/25/06, Mark Rages <markrages@gmail.com> wrote:
> Hi,
>
> The circuit I've attached is a staightforward op-amp amplifier with a
> gain of -10.
>
> For reasons outside the scope of this question*, I needed to add the
> resistor I've called Ra.
>
> In the traditional "virtual ground" method of analysis, Ra doesn't
> appear in the gain equation.  I tried Ra=10k in my circuit, and indeed
> it continued to work unchanged.  But I'm pretty sure if I set Ra=0 the
> circuit would stop working!
>
> To analyze this, I guess I will need a non-ideal op-amp model.  What
> is the important parameter to include?  Finite gain?  Offset voltage?
>
> Regards,
> Mark
> markrages@gmail
>
> * Because someone will want to know, it's to limit the voltage swing
> at an analog switch IC (not pictured).
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