*Stephen Woodward*

*EDN*

For at least four decades, dual-slope integrating A-to-D conversion has formed the core of most every digital multimeter and many industrial and instrumentation applications besides. Elegant in its simplicity, a DSADC (dual-slope analog-to-digital converter) employs an analog integrator coupled to a comparator and control logic to accumulate (integrate) the input signal, V_{IN}, for a fixed interval, T_{1} – comprising the first “slope” – then to switch the integrator’s input to a fixed negative reference, V_{REF}, to ramp the integrand back to zero – the second “slope” – while measuring the time required to do so, T_{2}. The input voltage is thus:

(1) |

This Design Idea applies a twist to the familiar algorithm: Simply reversing the order of signal and reference integration results in what I call a reciprocal dual-slope integrating ADC (RDSADC).

Here, V_{REF} is integrated for a fixed interval, T_{1}. Then the integrator input is switched to –V_{IN}, and the time T_{2} required to ramp back down to zero is measured. Thus:

(2) |

Given the similar equations, you might reasonably ask: “So what?” So this:

In equation 2, the conversion result is inversely proportional to time measurement T_{2 }and therefore to 1/V_{IN}, and differential calculus tells us that the rate of change of inverses varies, not linearly, but as the square of the inverse of the measured value, i.e.,

(3) |

The payoff is therefore a nonlinear conversion measurement that maintains high resolution for low amplitude inputs without any need for auto-ranging of the V_{IN} scale factor. A practical implementation of the RDSADC is shown in Figure 1. It converts inputs in the 10-bit range of 1 mV to 1 V while maintaining a 10-bit resolution at both extremes: 1 mV resolution at V_{IN} = 1 V, and 1 µV resolution at V_{IN} = 1 mV. This translates to a 1,000,000:1, 20-bit dynamic range with only a 15-bit 32k count resolution for T_{2}. In other words, a 20-bit dynamic range is achieved with only a 15-bit count, for a 32:1 improvement in conversion time over a similar resolution conventional DSADC. In fact, V_{IN} can go a bit negative, and all the way to 5 V at reduced resolution.

Figure 1. |
RDSADC reverses the usual order of integration to geta big increase in dynamic range. |

Here’s how it works:

The RDSADC cycle begins with connection of V_{REF} to the “+” input of integrator A2 (pin 3) by S1 through the R4/(R3 + R4) voltage divider, and integration during interval T_{1}, ending when V_{2} = V_{REF}, switching comparator A1’s output low (Figure 2).

Figure 2. |
RDSADC timing diagram:T _{1}: 1 ms (V_{REF }integration)T _{2}: 1-32 ms (V_{IN} integration)Count frequency: 1 MHz Sample rate: 30-500 Hz |

S1 then lets A2’s “+” input drop *nearly* to ground (more on that later), while S2 switches A2’s “-” input nearly to V_{IN} through R1. V_{2 }then ramps downward at a rate _{nearly }proportional to V_{IN}, defining counting interval T_{2}. Arrival of V_{2 }at the low threshold of A1 terminates T_{2}, completing the ADC cycle and beginning a new one, ad infinitum.

About those *nearlies*: Astute readers will have noticed that during T_{2}, when S1 removes V_{REF} from A1’s “+” input, a 42 mV positive bias is created by R5. The purpose of this bias is to keep A2’s output alive all the way down to the end of the T_{2} slope despite use of a unipolar power supply.

Also during T_{2}, R2 creates an effective 32 mV bias^{1}) to ensure that T_{2} remains finite (never more than 32 ms), even when V_{IN} approaches zero. Thus:

(4) |

This idealized arithmetic ignores real-world tolerances like A1 and A2 input offsets, V_{REF} accuracy, and resistor variations, but these imperfections can be easily compensated computationally with a simple two-point V_{FULLSCALE} and V_{ZERO} calibration.

^{1)} The 32 mV comes from the R1-R2 voltage-division of the 2.5 V V_{REF} (50 mV), which provides 1.6 µA (32 mV / 20 kΩ) of offset current to the V_{IN} / 20 kΩ input current, minus the “keep-alive” bias provided by divider R3-R5 (18 mV). Hence 50 mV – 18 mV = 32 mV.

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