# A high gain Transimpedance Amplifier for photodiodes

|# Introduction

The purpose of this article is to describe a simple design of a high gain transimpedance amplifier for photodiodes. Transimpedance amplifiers(TIAs) are commonly used to translate the current output of photodiodes and other sensors into a voltage. The most straightforward implementation of a TIA is with a feedback resistor from output to the inverting input of an operational amplifier. Although this circuit is very simple, it is still requires careful trade-offs among noise, gain and stability.

A generic opamp transimpedance amplifier (TIA) is shown below:

The detector is connected to the inverting input which is held at virtual ground due to the grounded non-inverting input. The photo-current flows through the feedback resistor π π leading to an output voltage equal to ββπ πππβ. πΆπ provides compensation for the effects of the input node capacitance and stabilises the circuit.

The gain of the transimpedance amplifier is set by the feedback resistor; the higher the value of the resistance, the higher is the gain. However, this is at the expense of bandwidth. The feedback compensating capacitor also affects the bandwidth. Overcompensating the TIA, with a feedback capacitance larger than required to stabilise the TIA, will unnecessarily reduce the bandwidth.

A high gain TIA design while maintaining a wide bandwidth is achievable if the Gain-Bandwidth product of the operational amplifier is high. The OPA657 operational amplifier from Texas Instruments boast a 1.6 GHz gain-bandwidth product. Having a high 1.6-GHz gain bandwidth product gives greater than 10-MHz signal bandwidths up to gains of 160 V/V (44 dB).

## High Gain Transimpedance Amplifier Schematic

The circuit was assembled with a feedback resistor of 200 kohms. The assembled PCB is also shown.

## Circuit response

The frequency response of the TIA was measured using a network analyser with a 10 pF capacitance connected to the input to represent the junction capacitance of the photodiode.

With no feedback capacitance, peaking is clearly visible in the response. With a capacitance of 0.2 pF and 0.5 pF, a flat response is observed. With the 0.5 pF capacitance, the circuit is overcompensated, hence a reduced bandwidth is obtained.

A reasonably high bandwidth and gain are obtained with minimal design, as shown in the frequency response.

## Analytical Analysis

Consider the following figure, where the photodiode is represented by a current source I_{ph}, a shunt resistor r_{s} and a junction capacitor C_{j}

Using a first order model for the operational amplifier open loop gain given by:

..the transimpedance of the circuit (V_{out}/I_{ph}) can be derived numerically and is equal to:

and the damping factor is equal to:

Using the following parameters, where A_{0} is the OPA657 DC open loop gain andΒ Ο_{0} is the time constant of the OPA657

c_{j} := 10 pF; R_{f} := 200k; A_{0} := 3162; r_{s} := 1G; Ο_{0} := 0.89837e-6

The circuit frequency response can be obtained for different values of C_{f}:

With C_{f} := 0.1pF, a damping factor of ΞΎ = 0.4366194372 is calculated and the numerical response looks like:

As observed with the measured response, the numerical frequency response also shows a clear peaking which will results in oscillations of the circuit output.

Increasing C_{f} to 0.2 pF reveals a flat response as expected:

The calculated damping factor ΞΎ is 0.8499125050 which is above critical damping factor of 0.7071, hence gives a flat response.

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