# How does this circuit work?

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#### an_82

##### Member level 2
I studied a paper attached with this post . I have a question about Fig. 3 which is also attached where a topology to realize multiplier circuit has been presented:

How can we apply "iin1" to "EOTA1"? In the paper it is mentioned that "gmT1" has a direct proportion to "IBE1", when we change "IBE1", "io1" changes and since "iin1= io1", "iin1" changes. If we apply "iin1" ideally, it seems that "io1" cannot change. Could you please explain how we apply input signal and how does it work with these conditions ? (I know all of the formulas, please explain applying of signals)

Thanks.

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#### LvW

an_82,

you have nothing to do than to combine the established OTA formulas in a correct way using

Un; Up: OTA input voltages at the negative resp. pos. input terminal
g1 ; g2 : OTA transconductances
Iabc=Control current into the external control node for determination of g (abc: amplifier bias current), in your case: Iabc=Ibe1 and Iabc=Ibe2+Iin2

Io1=-Iin1
Io1=-Un1*g1
Un1=Up2
Io2=Up2*g2

This results in Io2=Iin1*g2/g1

With g=Iabc/(2*Uth) you arrive at the given expression for Io2.
It is easy to find Io3 in the same way.

#### an_82

##### Member level 2
Dear LvW,

Thanks for your reply, but as I said I know all of the expressions. I mean that how can I simulate the circuit (in Hspice)? I putted CMOS transistor level of OTAs, then if I apply iin1 ideally, since iin1= -io1, io1 should be equal to applied iin1, while it can be changed by its "Iabc" !! how can I apply iin1 in the case that when I change "Iabc1", its "gm1" and consequently "io1" be change?

#### LvW

Thanks for your reply, but as I said I know all of the expressions. I mean that how can I simulate the circuit (in Hspice)? I putted CMOS transistor level of OTAs, then if I apply iin1 ideally, since iin1= -io1, io1 should be equal to applied iin1, while it can be changed by its "Iabc" !! how can I apply iin1 in the case that when I change "Iabc1", its "gm1" and consequently "io1" be change?

You are asking "how can I apply iin1"?
My answer: As a current source. Or did I misunderstand something?
Perhaps it helps, as a first step to simulate the circuit using IDEAL OTA blocks (VCCS) with varying gm values.
Real OTA`s have a separate pin to inject Iabc.

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