What is Capacitive Voltage Divider : Working & Its Applications

Generally in electronics, a voltage divider or a potential divider is a passive linear circuit, used to provide an output voltage that is a part of its input voltage. Here, voltage division is the outcome of distributing the input voltage between the voltage divider components. In a voltage divider circuit, two resistors are connected in series where the input voltage is given across the two resistors, and output is taken from the connection between two resistors. There are different types of voltage divider circuits available based on the application like resistive, inductive, low-pass RC filter, and capacitive voltage divider. This article gives brief information on one of the types of voltage divider namely – capacitive voltage divider and its working with applications.


What is Capacitive Voltage Divider?

A capacitive voltage divider is one kind of voltage divider circuit where capacitors are used as the voltage-dividing components. Similar to resistors, capacitors can also be used to form a voltage divider circuit so that voltage can be separated into parts of a circuit based on the capacitor value. Similar to a voltage divider circuit using resistors, capacitors are connected in series to form a voltage divider network with a voltage source.

Capacitive Voltage Divider
Capacitive Voltage Divider

How to Work Capacitive Voltage Divider?

Capacitive network dividers are more complex as compared to resistive networks because capacitors are reactive devices. So the resistance provided by capacitors in the circuit mainly depends on the input signal frequency. The capacitor resistance can be denoted with Xc and it is measured in ohms. The capacitor response is proportional to the capacitor’s capacitance value.

So, XC ∝ 1/C

If the frequency of the source current is low, the charging time of the capacitor will be increased. Similarly, if the frequency of the current source is high, then the charging time of the capacitor will be decreased. At last, we identify the frequency ‘F’, capacitive reactance is ‘Xc’ & capacitance value is ‘C’, then the equation will be;

XC ∝ 1/C

XC ∝ 1/f

The formula for capacitive reactance Xc = 1/2πfc

Where,

‘Xc’ is the reactance of a capacitor within ohms (Ω)

‘f’ is the frequency in Hertz (Hz)

‘C’ is the capacitance of a capacitor in farads (F)

‘π’ is the numeric constant (3.1416)

Capacitive Voltage Divider Circuit

The capacitive voltage divider circuit is shown below which is used to calculate the voltage divider rule of capacitors. In the following voltage divider circuit, two capacitors are connected in series with voltage sources like ‘Vs’. After that, the voltage source can be divided into two where one supply goes throughout the C1 capacitor and the other voltage goes throughout the C2 capacitor. Additionally, VC1 in the circuit denotes voltage throughout the C1 capacitor whereas VC2 is voltage throughout the C2 capacitor.

Capacitive Voltage Divider Circuit
Capacitive Voltage Divider Circuit

Hence the combined capacitance can be given as;

1/Ceq = 1/C1 + 1/C2

Ceq = C1C2/C1 + 1/C2

The amount of charge provided through the source Q = Ceq Vs, which is basically

Q = (C1C2/C1 + 1/C2) Vs

The voltage at ‘C1’ capacitor is Vc1

VC1 = Q1/ C1

VC1 = (C1C2/C1 + C2) x Vs/C1

VC1 = Vs/(C1 + C2) x C2

The voltage at ‘C2’ capacitor is Vc2

VC2 = Q2/ C2

VC2 = (C1C2/C1 + C2) x Vs/C2

VC2 = Vs/(C1 + C2) x C1

So, individual voltage throughout a capacitor is a fraction of opposite capacitance that is multiplied through whole capacitance & voltage.

Example Problems

A capacitive voltage divider simply works with both the AC & DC but the formula for both the AC & DC is nearly the same. So the example problems of both the AC and DC capacitive voltage divider circuits are explained below.

Capacitive AC Voltage Divider Circuit Example

The example capacitive AC voltage divider circuit diagram is shown below. The voltage source is 120V; the frequency is 1500 Hz. The two capacitors in the circuit are simply connected in series where the first capacitor value VC1 3uF with capacitance Xc is 30ohms. The second capacitor value like VC2 is 1uF with capacitance Xc being 60ohms.

AC Voltage Divider Circuit
AC Voltage Divider Circuit

The output voltage drop for both the capacitors like VC1 and VC2 is,

The reactance of the 3uF capacitor is;

XC1 = 1/2πfC1 => 1/(2*3.142*1500*3*10^-6) => 10^6/28278 => 35 Ohms

Reactance of 1uF capacitor is;

XC2 => 1/2πfC2 => 1/(2*3.142*1500*1*10^-6) = 10^6/ 9426 => 106 Ohms

The complete capacitive reactance of this circuit is, XC= XC1+ XC2= 35Ω + 106Ω = 141Ω

The flow of current within the circuit is,

I = V/XC = 120V/141Ω = 0.85mA

The voltage drop across every capacitor is,

VC1 = I*XC1 = 0.85mA*35Ω = 29.75V

VC2 = I*XC2 = 0.85mA*106Ω = 90.01V

Capacitive DC Voltage Divider Circuit Example

The circuit diagram of the capacitive DC voltage divider is shown below. The voltage source is 9V and the two capacitors are connected in series where VC1 is 3uF and the VC2 is 1uF. Here, the DC voltage divider separates the voltage based on the formula like V = Q/C. If the frequency of the circuit is 12000Hz or 12 kHz, evaluate the output voltage of DC.

DC Voltage Divider Circuit
DC Voltage Divider Circuit

3uF capacitor’s reactance XC1 = 1/2πfC1 = 1/(2*3.142*12000*3*10^-6) = 10^6/226224 = 4.420Ω

1uF capacitor reactance XC2 = 1/2πfC2 = 1/(2*3.142*12000*1*10^-6) = 10^6/75408 = 13.26Ω

The circuit’s complete capacitive reactance can be calculated by using XC= XC1+ XC2 = 4.420Ω + 13.26Ω = 17.68 Ohms.

I = V/XC = 9V/17.68Ω = 0.50mA

The voltage drop across every capacitor is,

VC1 = I*XC1 = 0.50mA*4.420Ω = 2.21V

VC2 = I*XC2 = 0.50mA*13.26Ω = 6.63V

Note: Other capacitive voltage divider formula can also be used for CT = (C1*C2) /(C1+C2) and after that, XCT = 1/2πfCT.

Advantages and Disadvantages

The advantages of a capacitive voltage divider include the following.

  • Inexpensive.
  • Heat loss is less.
  • They work on either AC or DC.
  • Installation cost is low.
  • Frequency-dependent.
  • Capacitive voltage divider has many benefits like fast pulse signals measuring because of its wide bandwidth, fast response, stability & large voltage division ratio.

The disadvantages of capacitive voltage divider include the following.

  • Quite heavy.
  • Working efficiency can be reduced due to overheating.
  • Some voltage dividers only work with AC.

Applications

The applications of capacitive voltage divider include the following.

  • This kind of voltage divider is used to reduce the voltage to measure high-level voltage.
  • These are ideal for fast-rising voltages & pulses measurement.
  • In the microcontroller, it is used to measure the resistance of the sensor.
  • This voltage divider can be used as a logic level shifter circuit for interfacing various operating voltages.
  • These circuits are used in different electronics applications which range from Colpitts Oscillator circuits to capacitive touch-sensitive screens.
  • These voltage dividers are extensively used within electron beam accelerators to evaluate the high-voltage o/p signal in the ns (nanosecond ) range.
  • Simple capacitive voltage dividers are used to measure high voltage signals in the range of nano to microseconds.

Thus, this is all about an overview of capacitive voltage dividers with examples in AC and DC circuits. This circuit uses a potential difference & separates it while maintaining the voltage ratio. Here is a question for you, what is a resistive voltage divider?

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