Clear[zin, rf, kv, taup0,tauf,taui,uin,tabcd,cb,cis,respfull,respsim,cros1,crosstalk,itrs,ilost,ChargeRead,ChargeLost];

"ABCD input impedance in s domain";
zin=(rf/kv) ((1+s taup0)/(1+s tauf));
"voltage at preamplifier input in s domain for delta dirac current input";
"uin=\!\(\*FractionBox[\(1\), \(s\\ cb + \*FractionBox[\(1\), \(zin\)] + \*FractionBox[\(2\\ s\\ cis\), \(1\\  + \\ zin\\ s\\ cis\)]\)]\);""full expression";

uin=(zin/(1+s (cb+2 cis) zin));"simplified, assuming zero input impedance for neighboring channels)";

FullSimplify[uin];

"Simplified ABCD transfer function, no AC coupling";

tabcd=(tauf/(((1+s tauf))^2)) (1/(((1+s taui))^2));

"ABCD response simplified";
respsim= InverseLaplaceTransform[ tabcd,s,t,tauf>taui&&taup0>tauf&&taui>0];

"ABCD crosstalk (first neighbor)";
cros1=tabcd uin (1/((1/(s cis))+zin));
FullSimplify[cros1,tauf>taui&&taup0>tauf&&taui>0];
crosstalk= InverseLaplaceTransform[cros1,s,t];

"ABCD response including detector backplane";
respfs=tabcd uin (1/zin);
FullSimplify[respfs,tauf>taui&&taup0>tauf&&taui>0];
respfull= InverseLaplaceTransform[respfs,s,t];

"Current transfer to amplifier input";
itrs=uin (1/zin);
FullSimplify[itrs,tauf>taui&&taup0>tauf&&taui>0];
itrsresp=InverseLaplaceTransform[itrs,s,t];
"Current lost in cb and 2 x cis";
ilost= uin s (2 cis+cb);
FullSimplify[ilost,tauf>taui&&taup0>tauf&&taui>0];
ilostresp=InverseLaplaceTransform[ilost,s,t];

"Charge transfered to amplifier input";
ChargeRead=(∫_0^∞)itrsresp\[DifferentialD]t;


rf=80 (10^3);tauf=10 (10^(-9));taui=4 (10^(-9));
cb=4 (10^(-12));cis=7 (10^(-12));
taup0=53 (10^(-9));kv=1654;
"Response in readout channel"
FullSimplify[respfull]
"ExpToTrig[respfull]"
"Cross talk" 
FullSimplify[crosstalk]
"ExpToTrig[crosstalk]"
"Response for channel not loaded with the detector (reference)"
Plot[respsim,{t,0,160 (10^(-9))},Frame->True, GridLines->Automatic]
FindMaximum[respsim,{t,10 (10^(-9)),30 (10^(-9))}]
"Response for channel loaded with the detector"
Plot[respfull,{t,1 (10^(-9)),160 (10^(-9))},Frame->True, GridLines->Automatic]
FindMaximum[respfull,{t,10 (10^(-9)),30 (10^(-9))}]
"Cross talk"
Plot[crosstalk,{t,1 (10^(-9)),160 (10^(-9))}, PlotRange->{-0.04,0.04},Frame->True, GridLines->Automatic]
FindMaximum[Abs[crosstalk],{t,1 (10^(-9)),30 (10^(-9))}]
"current to the front end input"
Plot[itrsresp,{t,1 (10^(-9)) ,160 (10^(-9 ))},PlotRange->{-1.4 (10^7),2 (10^8)},Frame->True, GridLines->Automatic]
"Charge transfered to amplifier input;"
ChargeRead