For matching to occur, the input resistance of the amplifier (i.e., the op-amp only with Rf) should have a certain value which is Ra-Rsw=30 Ohm. Then the required Rf is given by
Rf = (1+a0)*(Ra-Rsw)
Don't know the said paper
, but this approach has nothing in common with regular OP or TIA circuit design. It's the reason for forcing loop gain to unreasonable low values.
There's no point of matching a source impedance by increasing Rf
respectively reducing the loop gain.
In case of doubt, the closed loop gain would be simply too high, causing output saturation.
Matching input impedance this way can be however done with amplifiers that have a low, well-defined gain, e.g. a LNA.
In case an OTA with resistive load is suited for you as amplifier with defined gain, an OTA could be used.
In a paper I found the use of an OTA+buffer ("opamp") as a baseband amplifier after the mixer. It uses resistive feedback and the source resistance is given by a series of the antenna and the switch impedance of the mixer. To first order, the amplifier can be descried as the ordinary "inverting opamp amplifier":
... it consists of a simple diff pair + source follower
If the switch you shown does Mixing, then the impedance matching equation is not simply what was mentioned earlier? Because the Mixer comes in, changing the entire scenario.
I'd say such an amplifier shouldn't be called an OTA, much less an opamp.
Probably the high bandwidth here is more important than the low loop gain (which isn't negative BTW).
I agree completely with erikl. An OP is a device that is operated with loop gain > 1 and an overall (closed loop) gain set by the feedback network.
Why dont you try a telescopic structure for TIA? It will mostly work. Or two stage amp as in the second paper you mentioned.
Input impedance of a TIA is 1/Gm. You can use any value of Rf depending on the conversion gain you want. You need to match 1/Gm of the TIA to 50 ohms.
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