# Capacitive Divider: Capacitive Voltage Divider

The capacitive voltage divider consists of two parallel conductive plates separated by insulators. The plate has a positive (+) charge and a negative (-) charge on the opposite side.

The capacitor is connected to the DC voltage, and when fully charged, the dielectric material (insulator) interferes with the flow between positive and negative charges. Such voltage dividers are not affected by changes in frequency.

## What is Capacitive Voltage Divider?

The capacitive voltage divider is a circuit used as a voltage-dividing component. The primary function of this type of circuit is to assign different quality voltages to other parts of the course. According to Ohm’s law, V = IR. Where V is voltage, I is current, and R is resistance.

The current flow in the series circuit is the same everywhere. The sum of all the output values ​​of the capacitive voltage divider is equal to the total voltage of the source.

A capacitive voltage divider is a circuit that takes one potential difference and divides it into two while maintaining the voltage ratio. A capacitive divider will have two capacitors in series with each other.

For example, if you have a 12 volts power supply and put four 1μF capacitors in series with each other, then the output of the capacitors will be 4 volts at half the current of 12 volts.

So, in brief,

A Capacitive Voltage Divider is a circuit that divides a potential difference while maintaining the voltage ratio.

## Working Principle of Capacitive Voltage Divider

The capacitor voltage divider forms a series of voltage divider networks where the current flow value of each division is the same. However, the voltage difference between the two ends of each voltage divider differs. Since voltage resistors do not change their resistance values ​​depending on the input frequency in the network, it works in both DC and AC circuits.

The capacitive network is more complex than the resistive network because capacitors are reactive. Xc marks the capacitor resistance. It is also measured in ohms. The reaction of a capacitor is proportional to the capacitance value of the capacitor.

The formula of it is XC ∝ 1/C. If the source current frequency is less, the capacitor charging time increases. If the frequency is high, the capacitor charging time decreases. Finally, we recognize the frequency is F, the capacitor reactance is Xc, and the capacitance value is C. The equation is,

• Xc ∝ 1/C
• Xc ∝ 1/f

The capacitive reactance formula is XC = 1/2πfC

Here is,

• XC = Reactance of a capacitor in ohms (Ω)
• f = Frequency in Hertz’s (Hz)
• C = Capacitance of a capacitor in Farads (F)
• π = Numeric constant (22/7 = 3.1416)

## Capacitive Voltage Divider Formula

Capacitive voltage dividers are used in many circuit applications.

A capacitive voltage divider is a circuit using two capacitors in parallel with the output connected to the alternating current (AC) input. The ratio between the output and input voltage is given by

Vout/ Vin = 1/(1+Cs/Cp)

Cs is the total Capacitance of all series-connected capacitors, and Cp is the total Capacitance of all parallel-connected capacitors. This provides an AC signal with a magnitude that varies in proportion to Vin but with an offset that depends on whether Cs or Cp has more Capacitance.

## Circuit Diagram of Capacitive Voltage Divider

A capacitive voltage divider works both the AC and DC. The formula for AC and DC is almost the same. Both of the circuit diagrams are given below with an explanation.

### Capacitive AC Voltage Divider Circuit

A capacitive AC voltage divider circuits picture is given below. The source voltage is 120, and the frequency is 2KHz or 2000Hz. The two capacitors are connected with a series circuit connection. The first (VC1) one is 2uF, and its Capacitance (XC) is 40Ω. The second (VC2) one is 1uF, and its Capacitance (XC) is 80Ω.

The calculation of the output voltage drop of both the VC1 and VC2 capacitors is,

Reactance of 2uF capacitor, XC1 = 1/2πfC1 = 1/(2*3.142*2000*2*10-6) = 39Ω

Reactance of 1uF capacitor, XC2= 1/2πfC2 = 1/(2*3.142*2000*1*10-6) = 79Ω

The total capacitive Reactance of a circuit is XC= XC1+ XC2= 39Ω + 79Ω = 118Ω

The current in the circuit is,

I = V/XC = 120V/118Ω = 1.02mA

Now, the voltage drop across each capacitor is,

VC1 = I*XC1 = 1.02mA*39Ω = 39.78V

VC2 = I*XC2 =1.02mA*79Ω = 80.58V

Note: Another calculating formula of CT is (C1*C2) /(C1+C2). And then XCT = 1/2πfCT.

### Capacitive DC Voltage Divider Circuit

A capacitive DC voltage divider circuits picture is given below. Here is the source voltage, 15V. The two capacitors are connected with a series circuit connection. The first (VC1) one is 2uF. The second (VC2) one is 1uF. DC voltage divider divides the voltage according to the formula of V=Q/C.

Calculate the DC output voltage if the circuit’s frequency is 16000Hz or 16kHz.

Solve:

Reactance of 2uF capacitor, XC1 = 1/2πfC1 = 1/(2*3.142*16000*2*10-6) = 4.97Ω

Reactance of 1uF capacitor, XC2 = 1/2πfC2 = 1/(2*3.142*16000*1*10-6) = 9.95Ω

The total capacitive Reactance of a circuit is XC= XC1+ XC2= 4.97Ω + 9.95Ω = 14.92Ω

I = V/XC = 15V/14.92Ω = 1.01mA

Now, the voltage drop across each capacitor is,

VC1 = I*XC1 = 1.01mA*5Ω = 5.03V

VC2 = I*XC2 =1.01mA*10Ω = 10.1V

Note: Another calculating formula of CT is (C1*C2) /(C1+C2). And then XCT = 1/2πfCT.

## Uses of Capacitive Voltage Divider

Capacitive voltage dividers are used the different purposes. Some of its critical uses of it are given below:

• A voltage divider is used to decrease the voltage for measuring high-level voltage.
• The voltage divider in the microcontroller helps measure the sensor’s resistance.
• A voltage divider is used as a logic level shifter circuit to interface different operating voltages.

Although a voltage divider has many purposes to use. But it has some restrictions. Both the advantages and disadvantages of it are given below:

• Almost no loss of heat.
• Moderate cost.
• Works both the AC and DC.
• Cheapest cost to install.
• Frequency-dependent.