Engineering Does this (textbook) circuit diagram contain a mistake?

[kostoglotov]

Homework Statement

[/B]
This circuit solves some differential equation, the question is asking for the equation based on the circuit diagram

imgur link: http://i.imgur.com/b1npQSK.png

Homework Equations

The Attempt at a Solution

I refer to the input terminal for -f(t)...the signal from it doesn't seem to pass through any resistor on its way into the inverting summer, so I've no way (I think) of finding how the signal from -f(t) is scaled in the summer.

Is this a mistake on the diagram? If not, what am I missing?

 

[Tom.G]

Could be a current input rather than a voltage input... or a mistake.

 

[LvW]

Yes - I am sure, it is a mistake. The right most amplifier must add up three signals (voltages) - and for this purpose another series resistor is necessary.

 

[Tom.G]

The right most amplifier must add up three signals (voltages)...

Where does the problem statement say that? Did you leave something out?

 

[LvW]

Where does the problem statement say that? Did you leave something out?

It is the purpose of the circuit to "solve differential equations".
Hence, it needs an input. Such an input (time domain) is shown as "-f(t) directly at the inv. terminal of an opamp, which - at the same time - receives the sum of two other voltages. However, this addition works only if f(t) also is connected through another resistor (remember the virtual ground principle).
Thus, without such a resistor the whole circuit makes no sense.

 

[Tom.G]

...this addition works only if f(t) also is connected through another resistor...

That input is acting as a transimpedance amplifier. It is a current input. You can use KCL to help wrap your head around it.
https://en.wikipedia.org/wiki/Transimpedance_amplifier

 

[LvW]

That input is acting as a transimpedance amplifier. It is a current input. You can use KCL to help wrap your head around it.
https://en.wikipedia.org/wiki/Transimpedance_amplifier

A "current input" is nothing else than a voltage input with a corresponding large source resistance (see my answer).
On the other hand - do you really assume that such a circuit (analog computer circuitry for solving differential equations) is intended to work with current in and voltage out? This would make no sense at all.