A Fully-Differential Switched-Capacitor Dual-Slope Capacitance-To-Digital Converter (CDC) for a Capacitive Pressure Sensor

Abstract

This article focuses on a proposed Switched-Capacitor Dual-Slope based CDC. Special attention is paid to the measurement setup using a real pressure sensor. Performance scaling potential as well as dead zones are pointed out and discussed. In depth knowledge of the physical sensor behavior is key to design an optimal readout circuit. While this is true for high-end applications, low-performance IoT (Internet of Things) sensors aim at moderate resolution with very low power consumption. This article also provides insights into basic MEMS (Micro-Electro-Mechanical-System) physics. Based on that, an ambient air pressure sensor model for SPICE (Simulation-Program-with-Integrated-Circuit-Emphasis) circuit simulators is presented. The converter concept was proven on silicon in a 0.13 μ m process using both a real pressure sensor and an on-chip dummy MEMS bridge. A 3.2-ms measurement results in 13-bit resolution while consuming 35 μ A from a 1.5-V supply occupying 0.148 mm². A state-of-the-art comparison identifies potential room for improvements towards hybrid solutions, which is proposed in subsequent publications already.

Keywords: CDC; Capacitance-to-Digital Converter; Dual-Slope; MEMS; SPICE model; auto-zero; electro-mechanical coupled simulation; noise-shaping; pressure sensor; switched-capacitor.

Figure 1

MEMS modeled as a variable single-ended parallel-plates capacitor: (a1) at rest position; (a2) at a displacement x with respect to rest position; and (b) lumped parameters model of a 1-DOF spring–mass–damper system with the balance of forces acting on the micro system.

Figure 2

(a) Equilibrium on the moving mass considering an electrostatic force; and (b) the corresponding charge balance with a voltage biasing scheme.

Figure 3

Schematic equivalent and physical MEMS sensor view.

Figure 4

SPICE model of one single MEMS pressure sensor cell.

Figure 5

MEMS die photograph (a); and equivalent model schematic based on sensor and reference cell arrays (b) without parasitic capacitance.

Figure 6

$\Delta C$ reading of sensor model (a); and sensitivity (derivative) (b).

Figure 7

Single-ended un-centered (a) and centered (b) linearized equivalent pressure sensor $\Delta C$ reading over application input range.

Figure 8

Implemented fully differential Switched-Capacitor direct CDC. Note: $DAC$ and ${\varphi }_P$ have single-ended representation for more simplicity.

Figure 9

Implemented timing diagram and data evaluation of $N=M=4$. Note: Non-overlapping signals are not shown and infinite OTA settling speed is assumed for more simplicity.

Figure 10

Chip photos: Package with air pressure hole (a); and opened package view including layout (b).

Figure 11

Chip size comparison. From left to right: one euro cent coin, real pressure sensor open package, real pressure sensor closed package, and on-chip dummy bridge ASIC packaged.

Figure 12

Motherboard attached to a daughter board with a real pressure sensor test chip docked to the ambient air pressure generator via pneumatic mechanics (a); an external reference generator (1.5 V from a 9 V block battery) buffer AD8034 and auxiliary digital output amplifier buffer ADN466 (b).

Figure 13

Long-term spectral approximation of on-chip dummy bridge measurement to reveal circuit characteristics such as noise-shaping, flicker-noise, tonal behavior and potential measurement disturbers (a); CDC system linearity plot (CDC + real pressure sensor): input pressure vs. digital reading and equivalent bridge capacitor difference, respectively. The pressure step size is 25 mbar and ${\sigma }_{filt}$ is after 1024 consecutive measurements (b).

Figure 14

Dead zone example within measurement around 400 mbar of a real pressure sensor MEMS bridge (a); Simulated dead zone with and without added dithering (b).

Figure 15

Performance scaling potential of measured CDC using 1024 consecutive measurements applying a on-chip capacitor dummy bridge at ≈−2 dBFS.

Figure 16

State of the art energy vs. resolution comparison.