Transimpedance Topology - from block diagram to schematic
A) Closed-loop gain:
Here are the equations which have to be combined to find Af=vout/is:
ib=ic/hfe=is-if (hfe=beta)
if=-(vout-vbe)/Rf with vout=-icRc (simplification: rce&gt;&gt;Rc, Rf&gt;&gt;Rc)
vbe=ic/gm (gm=transconductance Ic/Vt)
This gives you the ratio ic/is which leads to vout/is with vout=-icRc.
B) Open-loop gain
Ao=vout/is=-icRc/is=-hfeRc
C) Loop gain and feedback factor
If you compare both results from A) and B) it is quite simple to derive the expressions for the loop gain and the feedback &quot;factor&quot; K (which is given in 1/Ohm). Just compare the closed loop gain Af with Af=Ao(1+KAo).
EDIT: Details to A):
ib=ic/hfe=is-if=is+(vout-vbe)/Rf=is-icRc/Rf-vbe/Rf=is-icRc/Rf-ic/gmRf
From this: ic/is=1/[1/hfe + (Rc+1/gm)/Rf] with 1/gm&lt;&lt;Rc.
ic/is=hfe/(1+hfeRc/Rf)