# 3-bit Flash Analog to Digital Converter with Example Circuit

In this tutorial, we will discuss the workings of a flash ADC. A flash ADC, or flash analog-to-digital converter, is the fastest type of ADC among all the other ADCs. It is also known as a parallel analog-to-digital converter. It comprises high-speed comparators, resistive voltage divider circuits, and a priority encoder. The tutorial is a complete guide that includes its workings, advantages, disadvantages, and applications in the market.

An N-bit flash ADC consists of two powered N-1 comparators, two powered N numbers of matched resistors, and a priority encoder. The block diagram for the concept is provided below:

### Main Components of Flash ADC

Before understanding the workings of the flash ADC, we should have knowledge of its components. A list of all the components of a flash ADC is provided below.

• Resistor voltage divider circuit
• Comparator
• Priority encoder

Now let’s look at these components of flash ADC in more detail in the section below.

#### Resistor Voltage Divider Circuit

The resistive voltage divider is a simple circuit network of resistors that scales down an input voltage connected to it. It happens because of the distribution of the input voltage among all the resistors. This circuit is useful for producing a reference voltage or stepping down the magnitude of a high voltage. We can derive the general formula for the circuit using Kirchhoff’s laws.

If two resistors are connected in series, then the formula is as follows:

Vout = R2 x Vin / R1 + R2

#### Comparator

The comparator is a basic operational amplifier that compares two analog voltages, or an input voltage, to a reference voltage. Its output is in the form of a binary signal. The comparators are mostly part of devices that need digitization of their input voltage.

The workings of a comparator are quite simple. The input voltage connects to the positive end, while the other voltage, or reference voltage, connects to the negative end of the comparator.

If V+ > V-, then Vout will be 1, and Vout will be pulled low if V+ < V-.

#### Priority Encoder

An encoder is a logic circuit that comes with two powered N inputs. It gives the binary code with respect to the corresponding high input. It produces errors if more than one input is in the high state. So, to counter this problem, the flash ADC uses a priority encoder. The priority encoder does not produce ambiguous results even if two or more inputs are in a high state simultaneously. Instead, it delivers the binary code on a priority basis. The priority mechanism can either be ascending or descending.

Let’s consider N inputs, with the Nth input being the highest priority input. If three inputs, i.e., N-1, 4, and 2, are high at the same time, then the priority encoder will generate a binary code corresponding to the N-1 input line.

## 3-Bit Flash ADC Example Circuit

To grasp the concept and better understand it, we will study a 3-bit flash ADC. This consists of seven comparators, a resistive voltage divider circuit that contains eight series resistors, and a priority encoder. We apply the input analog voltage to the positive terminal of the comparator and the reference voltage to the negative end of the comparator.

### Reference Voltage Formula

Let us suppose that V1 is applied to the first comparator, and then this V1 can be calculated as:

V1 = R x Vref / R + 7R
V1 = Vref / 8

Now consider V2 as the reference voltage for comparator number 2. So we can calculate the V2 as:

V2 = (R + R) x Vref / 8R
V2 = 2 x Vref / 8

Similarly, by voltage dividing, we can find the reference voltages of each comparator.

These reference voltages of each comparator reveal that there is a difference of one least significant bit among each of the reference voltages.

1 LSB = Vref / 8

Each comparator compares the input voltage to the reference voltage accordingly. Here are two cases:

If the input voltage is less than the reference voltage of the comparator, then the output of the comparator is low. Whereas if the input voltage is greater than the reference voltage of the particular comparator, then its output will be high.

The priority encoder is dependent on these comparators. The outputs of the comparators determine the binary code produced by the encoder.

### Reference Voltage Calculation

To completely comprehend the working of the flash ADC, we take an example reference and input voltage, i.e., Vref = 8 V and Vin = 3.3 V, respectively.

Using the formula for specific measurements, we can calculate V1 as follows:

V1 = R x 8 V / R + 7R
V1 = 8 Vf / 8
V1 = 1 V

Hence, we can calculate all the reference voltages using the voltage divider formula provided in the table above.

V2 = 2 V
V3 = 3 V
V4 = 4 V
V5 = 5 V
V6 = 6 V
V7 = 7 V

The analog input voltage is compared with all the comparator’s reference voltages of the Flash analog to digital converter. After comparison, we notice that the reference voltages of the first three comparators, i.e., 1 V, 2 V, and 3 V, are less than the 3.3 V input. That is why the output of the first three comparators is high while the remaining comparators are in a low state.

The outputs of these comparators become the inputs of the priority encoder. We can see that there are seven reference voltages. Hence, the 8th input line is connected to logic 1 and is given the least priority. It means that it is a descending-order priority encoder. This helps in the case where all the comparator’s output voltages are zero. Hence, importance will be given to the higher-priority outputs, so the encoder generates an all-zero output.

As three input lines of the encoder are high at the same time, priority will be given to the third input, and a corresponding output binary code is generated.

### Sample & Hold Circuit

This is the process through which a flash analog-to-digital converter takes a continuous analog input and converts it into a binary output. For this ADC to be accurate, the input voltage must not vary; otherwise, it affects the output and produces errors. To tackle this, the flash ADC is used in combination with a sample and hold circuit. The respective circuit samples the input circuit and holds that sample circuit until the conversion is complete and the next signal arrives.

It is the optimized version of a full-flash ADC. The advantages of this configuration are that it requires less die area, less power consumption, and the same resolution as the full-flash ADC.

### Working Principle

Consider an 8-bit ADC. The schematic for the visual is as follows:

It consists of two 4-bit flash ADCs and a DAC in combination with a sample & hold circuit and a subtractor. First, the sample & hold circuit samples the input voltage for the first 4-bit ADC. This ADC gives out the binary code, which will be the MSB of the final binary output. It is fed into the DAC, which converts the signal back to an analog signal to be used as a reference voltage. The output of the subtractor is the input of the second ADC and gives out the LSBs of the final binary output.

Therefore, the same resolution is achieved with only 30 comparators.

`2 x (2 ^ N - 1) = 30`

Therefore, the same resolution is achieved with only 30 comparators. Though it has some genuine advantages, this configuration has a slow conversion speed compared to the full-flash ADCs.

• It is the fastest ADC and is popular in high bandwidth applications.

• These ADCs are more power-consuming as compared to ADCs implemented with different techniques.
• It has a limited resolution of up to 8 bits.
• The increase in bits leads to a large die area. With an 8-bit resolution, it needs a die area big enough to accommodate 255 comparators (2 ^ N-1).
• The resistors and comparators need to match to provide an accurate reference voltage to the comparators via the voltage divider network.

## Conclusion

In conclusion, this tutorial provides an in-depth overview of the flash ADC circuit. It covers details such as the introduction and its components. After this, an example of a 3-bit flash ADC and a half-flash ADC helps us better understand the concept and their workings. At last, this tutorial covers the advantages, disadvantages, and application of a flash ADC. Hopefully, this tutorial was helpful in broadening your knowledge