Integrating ADC

An integrating ADC is a type of analog-to-digital-converter that converts an unknown input voltage into a digital representation through the use of an integrator. In its most basic implementation, the unknown input voltage is applied to the input of the integrator and allowed to ramp for a fixed time period (the run-up period). Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero (the run-down period). The input voltage is computed as a function of the reference voltage, the constant run-up time period, and the measured run-down time period. The run-down time measurement is usually made in units of the converter's clock, so longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution.

Converters of this type (or variations on the concept) are able to achieve high resolutions (8.5 digits, or 28 bits, in the case of the Agilent 3458A digital multimeter), but often do so at the expense of speed. The Agilent 3458A, for example, only achieves its highest resolution at a rate of six samples per second. For this reason, these converters are not found in audio or signal processing applications. Their use is typically limited to digital voltmeters and other instruments requiring highly accurate measurements.

Basic Design

The basic integrating ADC circuit consists of an integrator, a switch to select between the voltage to be measured and the reference voltage, a timer that determines how long to integrate the unknown and measures how long the reference integration took, a comparator to detect zero crossing, and a controller. Depending on the implementation, a switch may also be present in parallel with the integrator capacitor to allow the integrator to be reset (by discharging the integrator capacitor). The switches will be controlled electrically by means of the converter's controller (a microprocessor or dedicated control logic). Inputs to the controller include a clock (used to measure time) and the output of a comparator used to detect when the integrator's output reaches zero.

The conversion takes place in two phases: the run-up phase, where the input to the integrator is the voltage to be measured, and the run-down phase, where the input to the integrator is a known reference voltage. During the run-up phase, the switch selects the measured voltage as the input to the integrator. The integrator is allowed to ramp for a fixed period of time to allow a charge to build on the integrator capacitor. During the run-down phase, the switch selects the reference voltage as the input to the integrator. The time that it takes for the integrator's output to return to zero is measured during this phase.

In order for the reference voltage to ramp the integrator voltage down, the reference voltage needs to have a polarity opposite to that of the input voltage. In most cases, for positive input voltages, this means that the reference voltage will be negative. To handle both positive and negative input voltages, a positive and negative reference voltage is required. The selection of which reference to use during the run-down phase would be based on the polarity of the integrator output at the end of the run-up phase. That is, if the integrator's output were negative at the end of the run-up phase, a negative reference voltage would be required. If the integrator's output were positive, a positive reference voltage would be required.

The basic equation for the output of the integrator (assuming a constant input) is:

Assuming that the initial integrator voltage at the start of each conversion is zero and that the integrator voltage at the end of the run down period will be zero, we have the following two equations that cover the integrator's output during the two phases of the conversion:

The two equations can be combined and solved for V_in, the unknown input voltage:

From the equation, one of the benefits of the dual-slope integrating ADC becomes apparent: the measurement is independent of the values of the circuit elements (R and C). This does not mean, however, that the values of R and C are unimportant in the design of a dual-slope integrating ADC (as will be explained below).

Note that in the graph to the right, the voltage is shown as going up during the run-up phase and down during the run-down phase. In reality, because the integrator uses the op-amp in a negative feedback configuration, applying a positive V_in will cause the output of the integrator to go down. The up and down more accurately refer to the process of adding charge to the integrator capacitor during the run-up phase and removing charge during the run-down phase.

The resolution of the dual-slope integrating ADC is determined primarily by the length of the run-down period and by the time measurement resolution (i.e., the frequency of the controller's clock). The required resolution (in number of bits) dictates the minimum length of the run-down period for a full-scale input (V_in = − V_ref):

During the measurement of a full-scale input, the slope of the integrator's output will be the same during the run-up and run-down phases. This also implies that the time of the run-up period and run-down period will be equal (t_u = t_d) and that the total measurement time will be 2t_d. Therefore, the total measurement time for a full-scale input will be based on the desired resolution and the frequency of the controller's clock:

If a resolution of 16 bits is required with a controller clock of 10 MHz, the measurement time will be 13.1 milliseconds (or a sampling rate of just 76 samples per second). However, the sampling time can be improved by sacrificing resolution. If the resolution requirement is reduced to 10 bits, the measurement time is also reduced to only 0.2 milliseconds (almost 4900 samples per second).  

Limitations

There are limits to the maximum resolution of the dual-slope integrating ADC. It is not possible to increase the resolution of the basic dual-slope ADC to arbitrarily high values by using longer measurement times or faster clocks. Resolution is limited by:

• The range of the integrating amplifier. The voltage rails on an op-amp limit the output voltage of the integrator. An input left connected to the integrator for too long will eventually cause the op amp to limit its output to some maximum value, making any calculation based on the run-down time meaningless. The integrator's resistor and capacitor are therefore chosen carefully based on the voltage rails of the op-amp, the reference voltage and expected full-scale input, and the longest run-up time needed to achieve the desired resolution.
• The accuracy of the comparator used as the null detector. Wideband circuit noise limits the ability of the comparator to identify exactly when the output of the integrator has reached zero. Goerke suggests a typical limit is a comparator resolution of 1 milivolt.
• The quality of the integrator's capacitor. Although the integrating capacitor need not be perfectly linear, it does need to be time-invariant. Dielectric absorption causes errors.