Since T and V ref are fixed, the time that the down count takes is proportional to the input voltage. Meanwhile, the counter is counting up at a rate fixed by the precision clock frequency. How will we know when we get to zero?

One method to improve the resolution of the converter is to artificially increase the range of the integrating amplifier during the run-up phase. During the run-down phase, the switch selects the reference voltage as the input to the integrator. Or, more importantly, it has a dependence on the ratio of the two resistance values. We integrate the unknown voltage V in t for a fixed time T.

Additionally, measuring time precisely is easier than measuring potential precisely. By integrating, we average out the noise, thus getting a precise measurement of the input potential. In most cases, for positive input voltages, this means that the reference voltage will be negative. The simple, single-slope run-down is slow. 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. 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. Their use is typically limited to digital voltmeters and other instruments requiring highly accurate measurements. If we're clever and why wouldn't we be? In most variants of the dual-slope integrating converter, the converter's performance is dependent on one or more of the circuit parameters. In its basic implementation, the dual-slope converter, 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. The dual-slope method can be thought of analogously in terms of a rotary spring such as that used in a mechanical clock mechanism. The circuit diagram shown to the right is an example of how multi-slope run-up could be implemented. During the measurement of a full-scale input, steps to freedom neil anderson pdf the slope of the integrator's output will be the same during the run-up and run-down phases.

Now disconnect the input potential. Now let's translate that into electronics. Positive and negative reference voltages controlled by the two independent switches add and subtract charge as needed to keep the output of the integrator within its limits. Output from multi-slope run-up.

The run-up will have added some unknown amount of charge to the integrator. This still allows the same total amount of charge accumulation, but it does so over a smaller period of time. Sample and Hold Settling Time. Converters of this type can achieve high resolution, but often do so at the expense of speed.

While it is possible to continue the multi-slope run-up indefinitely, it is not possible to increase the resolution of the converter to arbitrarily high levels just by using a longer run-up time. This is often done internal to the converter itself by periodically taking measurements of the ground potential. Circuit diagram for a multi-slope run-up converter. Depending on the implementation, a switch may also be present in parallel with the integrator capacitor to allow the integrator to be reset. This equation represents the theoretical calculation of the input voltage assuming ideal components.

As mentioned above, the purpose of the run-up phase is to add an unknown amount of charge to the integrator to be later measured during the run-down phase. Likewise, the speed of the converter can be improved by sacrificing resolution. The time for the first-run down using the steepest slope is dependent on the unknown input i. Remember that there are multiple ways to format binary numbers? Then, in the other direction, with a fixed reference voltage producing a fixed rate of output voltage change with time measured by the same counter. The Q Format and Addition Examples Fixed-point representation allows us to use fractional numbers on low-cost integer hardware. Such a continuously-integrating converter is very similar to a delta-sigma analog-to-digital converter. That is, it allows an unknown amount of charge to build up on the integrator's capacitor. 