A linear and wide dynamic range transimpedance amplifier with adaptive gain control technique

Abstract

A linear and wide dynamic range transimpedance amplifier (TIA) for the pulsed time-of-flight imaging LADAR application has been designed and simulated in a 0.18 μm 3.3 V CMOS technology. Specific design techniques, including adaptive gain control technique to widen linear dynamic range, pseudo-differential structure of the front end to decrease the common-mode noise and noise minimization to improve SNR, have been proposed to achieve challenging designs goals with linear dynamic range of 5000:1, high transimpedance gain of 89 dB Ω, bandwidth up to 150 MHz, equivalent input-referred noise current less than 8 ${\text{pA}}/\sqrt {\text{Hz}}$, in 2 pF photodiode parasitic capacitance. The proposed TIA consumes 165 mW with 3.3 V power supply.

Appendix

The Fig. 8 shows the simplified the noise model of the proposed TIA, the transfer function from $I_{in}$ to the output ($V_{out}$) is found by using KCL method to be

$$\frac{{V_{out} (s)}}{{I_{in} (s)}} = R_{F} \times \frac{{A_{V1} }}{{1 + A_{V1} }} \times A_{V} \times \frac{1}{{1 + s\frac{{C_{tot} (R_{F} + r_{ds} )}}{{1 + A_{V1} }}}}$$

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where $A_{V} = A_{V2} A_{V3} A_{V4}$, $r_{ds}$ is output resistance of the push–pull inverter shown in Fig. 5(a). The gain from the noise source $\overline{I_{{n,R_{F} }}^{2}}$ to the output ($V_{out}$) is

$$\frac{{V_{out} (s)}}{{I_{{n,R_{F} }} (s)}} = R_{F} \times \frac{{A_{V1} }}{{1 + A_{V1} }} \times A_{V} \times \frac{{1 + s\frac{{C_{tot} r_{ds} )}}{{A_{V1} }}}}{{1 + s\frac{{C_{tot} (R_{F} + r_{ds} )}}{{1 + A_{V1} }}}}$$

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The gain from the noise source $\overline{I_{D,MN1}^{2}} + \overline{I_{D,MP1}^{2}}$ to the output ($V_{out}$) is found by using nodal analysis to be

$$\frac{{V_{out} (s)}}{{I_{n,D} (s)}} = r_{ds} \times \frac{{A_{V1} }}{{1 + A_{V1} }} \times A_{V} \times \frac{{1 + sC_{tot} R_{F} }}{{1 + s\frac{{C_{tot} (R_{F} + r_{ds} )}}{{1 + A_{V1} }}}}$$

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In order to refer the noise due to push pull inverter back to the input, we use above transfer function to obtain

$$\begin{aligned} \overline{I_{in,D}^{2}} = & \left( \overline{{I_{D,MN1}^{2}} + \overline{I_{D,MP1}^{2}} } \right)\left| {\frac{{V_{out} \left( s \right)}}{{I_{n,D} \left( s \right)}}} \right|^{2} /\left| {\frac{{V_{out} \left( s \right)}}{{I_{in} (s)}}} \right|^{2} \\ \, = \left( {\overline{I_{D,MN1}^{2}} + \overline{I_{D,MP1}^{2}} } \right)\frac{{1 + \omega^{2} (C_{tot} R_{F} )^{2} }}{{(g_{m} R_{F} )^{2} }} \\ \end{aligned}$$

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we use

$$\overline{I_{D,MN1}^{2}} + \overline{I_{D,MP1}^{2}} = 4kT\gamma g_{m}$$

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where $k$ is Boltzmann’s constant and $T$ is the absolute temperature. $\gamma$ is the channel noise factor,$g_{m} = g_{m,MN1} + g_{m,MP1}$. And we add to the input noise source that models the noise of the feedback resistor to obtain the total input-referred noise current, given by

$$\overline{I_{{in,R_{F} }}^{2}} = \frac{4kT}{{R_{F} }}\left[ {1 + \frac{\gamma }{{g_{m} R_{F} }}} \right] + \frac{4kT}{{g_{m} }}\omega^{2} C_{tot}^{2} \left[ {\gamma + \frac{1}{{g_{m} R_{F} }}} \right]$$

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normally, $\frac{\gamma }{{g_{m} R_{F} }} \ll 1$, then, we can obtain

$$\overline{I_{{in,R_{F} }}^{2}} \approx \frac{4kT}{{R_{F} }} + \frac{4kT}{{R_{F} }}\frac{{\omega^{2} C_{tot}^{2} }}{{g_{m}^{2} }} + 4kT\gamma \frac{{\omega^{2} C_{tot}^{2} }}{{g_{m} }}$$

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using the fact [20] that: $V_{eff} = \left| {V_{gs,MN1} - V_{th,MN1} } \right| = \left| {V_{gs,MP1} - V_{th,MP1} } \right|$, $g_{m} = g_{m,MN1} + g_{m,MP1} = \frac{3}{{2L^{2} }}V_{eff} \left( {\mu_{n} C_{GS,MN1} + \mu_{p} C_{GS,MP1} } \right),$we can write Eq. 19 as:

$$\overline{I_{{in,R_{F} }}^{2}} \approx \frac{4kT}{{R_{F} }} + \frac{16kT}{{9R_{F} }}\frac{{L^{4} \omega^{2} C_{tot}^{2} }}{{\left[ {V_{eff} (\mu_{n} C_{GS,MN1} + \mu_{p} C_{GS,MP1} )} \right]^{2} }} + \frac{8kT\gamma }{3}\frac{{L^{2} \omega^{2} C_{tot}^{2} }}{{V_{eff} (\mu_{n} C_{GS,MN1} + \mu_{p} C_{GS,MP1} )}}$$

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normally, $\gamma$ is derived to be equal to 2/3 [19], so, we rewrite the Eq. 20 as:

$$\overline{I_{{in,R_{F} }}^{2}} \approx \frac{4kT}{{R_{F} }} + \frac{16kT}{{9R_{F} }}\frac{{L^{4} \omega^{2} (C_{PD} + C_{PAD} + C_{GS,MN1} + C_{GS,MP1} )^{2} }}{{\left[ {V_{eff} (\mu_{n} C_{GS,MN1} + \mu_{p} C_{GS,MP1} )} \right]^{2} }} + \frac{16kT}{9}\frac{{L^{2} \omega^{2} (C_{PD} + C_{PAD} + C_{GS,MN1} + C_{GS,MP1} )^{2} }}{{V_{eff} (\mu_{n} C_{GS,MN1} + \mu_{p} C_{GS,MP1} )}}$$

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The minimum input-referred noise current of the proposed TIA can be obtain by sizing MN1 an MP1 with shortest channel length, assuming $W_{MP1} = 2W_{MN1}$, and $\mu_{n} = 2\mu_{p}$, then $C_{GS,MN1} = \frac{{C_{GS,MP1} }}{2}$. The total input-referred noise current can be approximately calculated by

$$\overline{I_{{in,R_{F} }}^{2}} \approx \frac{4kT}{{R_{F} }} + \frac{8kT}{9}\frac{{L^{2} \omega^{2} \left( {C_{PD} + C_{PAD} + 3C_{GS,MN1} } \right)^{2} }}{{V_{eff} \mu_{n} C_{GS,MN1} }}\left( {1 + \frac{1}{{2R_{F} }}\frac{{L^{2} }}{{V_{eff} \mu_{n} C_{GS,MN1} }}} \right)$$

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