EMI resisting MOSFET-only voltage reference based on ZTC condition

Abstract

Electromagnetic interference (EMI) can significantly degrades the performance of analog circuits, including voltage and current references, especially due to their limited power supply rejection. An EMI resistant MOSFET-only voltage reference is herein proposed, based on the MOSFET zero temperature coefficient (ZTC) vicinity condition. The ZTC condition is analytically derived through a continuous MOSFET model that is valid from weak to strong inversion, also a design methodology is presented. The final circuit is designed in a 130 nm process and occupies around 0.0075 mm$^{2}$ of silicon area while consuming just 10.3 $\upmu$W. Post-layout simulations present a 395 mV reference voltage ($V_{REF}$) with a effective temperature coefficient ($TC_{eff}$) of 146 ppm/°C, for a temperature range from −55 to +125 °C. A 4 dBm (1 $V_{pp}$ amplitude) EMI source injected into the power supply, according to direct power injection standard [1], results in a maximum DC Shift and peak-to-peak ripple of −1.7 % and 35.8 m$V_{pp}$, respectively. The proposed voltage reference has already been fabricated and is under preliminary measurements, presenting a maximum variation of 21 mV for a 600 mV minimum supply.

Appendices

Appendix 1 $\phi _{t}$ Thermal Sensitivity

Knowing that $\phi _{t}=\frac{kT}{q}$ [21], its derivative with respect to T is then

$$\frac{\partial \phi _{t}}{\partial T} = \frac{k}{q}$$

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Multiplying both numerator and denominator by temperature (T),

$$\frac{\partial \phi _{t}}{\partial T} = \frac{k}{q} \left( \frac{T}{T} \right) = \frac{\phi _{t}}{T}$$

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Appendix 2 $\mu (T)$ Thermal Sensitivity

From Eq. (8) and repeated below, the low-field mobility dependence on temperature is given by

$$\mu (T) = \mu (T_0) \left( \frac{T}{T_0} \right) ^{\alpha _{\mu }}$$

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if one differentiates with respect to temperature, we get

$$\frac{\partial \mu }{\partial T} = \frac{\partial }{\partial T}\left( \mu (T_0) \left( \frac{T}{T_0} \right) ^{\alpha _{\mu }} \right) = \frac{\mu (T_0)}{(T_0)^{\alpha _{\mu }}} \frac{\partial }{\partial T}(T)^{\alpha _{\mu }}$$

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As $\frac{\partial }{\partial x}(x^{a}) = a x^{a-1}$, we get

$$\frac{\partial \mu }{\partial T} = \frac{\alpha _{\mu }\mu (T_0)}{(T_0)^{\alpha _{\mu }}} (T)^{\alpha _{\mu }-1}$$

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Multiplying both numerator and denominator by temperature (T),

$$\frac{\partial \mu }{\partial T} = \frac{\alpha _{\mu }\mu (T_0)}{(T_0)^{\alpha _{\mu }}} (T)^{\alpha _{\mu }-1} \frac{T}{T} = \frac{\alpha _{\mu }}{T} \underbrace{ \mu (T_0) \left( \frac{T}{T_0} \right) ^{\alpha _{\mu }}}_{ \mu (T) }$$

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Then,

$$\frac{\partial \mu }{\partial T} = \frac{\mu \alpha _{\mu }}{T}$$

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Appendix 3 $\phi _{t}$ Second Order Thermal Sensitivity

Knowing that $\phi _{t}^2= \left( \frac{kT}{q} \right) ^2$ [21], then its derivative with respect to T is

$$\frac{\partial \phi _{t}^2}{\partial T} = \left( \frac{k}{q} \right) ^2 2T$$

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Multiplying both numerator and denominator by temperature (T),

$$\frac{\partial \phi _{t}^2}{\partial T} = \left( \frac{k}{q} \right) ^2 2T \left( \frac{T}{T} \right) = \left( \frac{2}{T} \right) \underbrace{ \left( \frac{kT}{q} \right) ^2 }_{ \phi _t^2}$$

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Then,

$$\frac{ \partial \phi _t^2}{ \partial T} = \frac{2}{T}\phi _t^2$$

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