Only one circuit is needed to meet system resolution and 12-bit accuracy requirements

In general, handheld instruments, data loggers, in-vehicle and monitoring systems require a low-cost, high-precision, high-system resolution, multiplexed system. Can all of these requirements be integrated into one circuit? A system that can handle these diverse requirements requires a multiplexer, gain block and an analog-to-digital converter (ADC).

One possible solution to this problem is a 10-channel, programmable amplifier (PGA) that works in conjunction with a medium-speed 12-bit SAR ADC (see Figure 1). This single-supply, 10-channel PGA has a rail-to-rail input/output with a gain adjustment range of 1 V/V to 200 V/V. The PGA's low noise performance of 12 nV/Hz @ 10 kHz is suitable for 12-bit systems. The analog interface between the two devices includes an operational amplifier (OPA) in a buffer structure and an R/C circuit. The 12-bit ADC is a capacitive SAR ADC with inherent sample and hold. The converter requires an R/C circuit that simplifies the charging action of the ADC input structure.

Figure 1. This system uses a multiplexed PGA and an op amp to drive a 12-bit converter.

The calculated PGA noise value (referred to output (RTO)) is equal to the PGA noise density at 10 kHz (12 nV/√Hz) multiplied by the square root of the PGA closed-loop bandwidth times √(p/2). Multiples of √(p/2) account for noise in frequency regions outside the PGA bandwidth. This value is then multiplied by the PGA gain. Equation 1 uses a PGA gain of 16 V/V:

PGArms-noise = 12 nV/ÖHz * Ö (1.6 MHz * Ö/2) * 16 V/V = 0.304 mV (rms) Equation 1

The ADC noise generated by the converter is 431 mV (rms), which is well below the 1 LSB or 1.22 mV of this 5 V system. The buffer amplifier noise is 39 mV (rms), which contributes little to no noise to the system.

The combined noise of the PGA, OPA, and ADC is 529 mV (rms), which is still less than 1 LSB for a 12-bit converter. This value is calculated using a square root equation, Equation 2:

Noise (RTO) = Ö (PGArms-noise2 + OPArms-noise2 + ADCrms-noise2) Equation 2

The equivalent 12-bit accuracy (Equiv12-bit) of this system is 0.432 LSBs with a PGA gain of 16 V/V (see Equation 3).

Equiv12-bit = (NoiseRTO * 2N)/FSR, {where N = 12 and FSR = 5 V/V} Equation 3

If we look at the system over a PGA gain range of 1-200 V/V, we see that the PGA noise dominates the circuit. Once the PGA gain exceeds ~125 V/V, the system no longer meets the 12-bit accuracy criteria. However, this can be improved by reducing the voltage size of the system reference input LSB (see Figure 2). The tradeoff for getting a smaller LSB is reducing the effective number of bits (ENOB) of the system.

Figure 2. System accuracy is better than 0.01% with a PGA gain of 1–125 V/V.

When the PGA gain is 125-200 V/V, the system accuracy is better than 0.02%.

The system shown in Figure 1 provides adequate PGA gain range when 12-bit accuracy is required and equally adequate gain range when high system resolution is required.