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[Moved]: problem with calculating noise gain bandwidth and transimpedance

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ultrasonic.1991

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hi I'm reading a paper about a transimpedance amplifier. in the paper says The transimpedance gain transfer function and the bandwidth can be calculated from the small signal model (the formulas are attached in the below pictures. i don't know how to get to the functions given below from small signal. i tried every way possible.can anyone help me ? is there a way i could get to these formulas by a program ?
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i figured out how to calculate transimpedance function but i cant get to the noise phrases by small signal. can anyone help me about noise phrases ?
 

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