# Tracking Type ADC -Up/Down Counter Analog to Digital Converter

In the last tutorial, we have learned about counter-type ADC which is a single slope ADC with incrementing slope. Further, the counter value only increments up until it matches with the analog input voltage value. In simple words, the counter resets to zero after every single conversion. The counter counts only upward. Hence, it has only a positive slope and for other direction, the slope is simply zero. In order to resolve this issue, we can use a tracking type ADC.

Tracking type ADC is an improved version of counter type analog to digital converter. The counter type analog to digital converter has a drawback that it resets itself for every new conversion. It starts its count again from zero onwards for every other conversion. Even a small change in the input voltage leads to the device reset. Therefore, to cater to this issue, another type of analog to digital converter based on a similar schematic as a counter type analog to digital converter was introduced which is known as a tracking type analog to digital converter. This post is an overview of the tracking type analog to digital converter, working, applications, advantages, and disadvantages.

The schematic diagram of tracking type analog to digital converter and counter type is alike except for the counter. The tracking type analog to digital converter consists of a comparator, control circuit, an up-down counter, a digital to analog converter, and an output latch circuit that gives out the final binary outputs.

The comparator receives two voltages i.e. input voltage and the reference voltage. The input analog voltage is applied to the non-inverting end of the comparator whereas the reference voltage is applied to the negative or inverting end of the comparator. This reference voltage is basically the output of the digital to analog converter that gets compared with the given input voltage and determines the state of the comparator.

### If Vin > Vdac

When the respective analog to digital converter is powered on, the output of the digital to analog converter is zero. When this is compared with the applied voltage, the comparator gets high and the counter starts its counting from zero onwards. It means that it starts counting in the upward direction. In return, the output of the digital to analog converter starts to increase slowly.

### If Vin < Vdac

But when the continuous input voltage is less than the output of the digital to analog converter, the comparator goes from high to low state at that particular time. This enables the up-down counter to start its counting in the reverse direction that is in the down direction instead of resetting itself just like the counter type ADC.

Once again when the output of the digital to analog converter becomes greater than the input voltage, the comparator becomes high and the counter enters up count mode and vice versa the counter enters the down count mode. The condition for whether the counter counts in an upward or downward direction depends on the input voltage and the process keeps on repeating.

This analog to digital converter keeps the track of the input voltage consistently for its functionality therefore it is called a Tracking type analog to digital converter.

### Output Latching

The output of the counter is latched whenever the comparator transits its output. It means that every time when the output of the comparator transitions from high to low or low to high state then the binary output of the up-down counter is latched.

## Conversion Time

Here is the visual pattern of the output of the digital to analog converter:

The graph shows that in the beginning, the output of the digital to analog converter was increasing gradually until it reached and tracked the input voltage.

The maximum conversion time at this point

`Tc(max) = (2^N-1)Tclk`

Where N is the number of bits of analog to digital converter and Tclk is the duration of the clock pulse.

This depicts that when the changer in the input voltage becomes equal to the full-scale voltage of the digital to analog converter the up-down counter moves from all zeros to all ones (0000—->1111) and from all ones to all zeros (1111—->0000).

The conversion time of tracking analog to digital converter depends upon the changes of the input signal. If the input voltage changed rapidly, the conversion time would be more  while the conversion time will be less if the input changes gradually. It is shown in the figure below:

If the average conversion time is to be compared with the counter type ADC then tracking type analog to digital converter has lesser conversion time.

## Sampling Time

The conversion time plays an important role in determining the sampling time of the analog to digital converter. It is the time after which the input signal is to be sampled. Generally, the sampled time of an analog to digital converter is equal to the sum of conversion time and additional time delay.

`Ts = Tc + Tdelay`

Where Tdelay is the acquisition time and ADC components delay.

In order to sample the applied input signal at uniform intervals then uniform sampling time should be equal to the maximum conversion time if the additional time delay is not considered.

`Ts = Tc(max)`

## Sampling Frequency

It is the number of samples per second taken from a continuous analog signal to form discrete signals.

The sampling frequency is equal to the inverse of the sampling time.

`fs = 1/Tc(max)`

If fs is the sampling frequency then the maximum input frequency is

```fmax = fs/2
fmax = 1/(2*Tc(max))```

The maximum frequency is obtained through the Nyquist theorem which states that the sampling frequency should be twice the maximum input frequency.

The general equation shows that the maximum frequency is inversely proportional to the maximum conversion time if the additional delay is not considered. This result should be kept in mind while designing this analog to digital converter.