Capacitive voltage divider

A capacitive voltage divider is used to measure high electrical voltages . A calculation or implementation takes place via a serial arrangement of at least two capacitors . It is constructed like an ohmic voltage divider , but uses capacitors instead of ohmic resistors and is only suitable for AC voltage .

example

In a circuit there are two capacitors, C _v and C _m (measuring capacitance). The measurement capacitance should be selected to be relatively large in relation to C _v in order not to have a falsifying effect on the actual circuit. In a series connection , the electrical charges of the individual capacitances are the same. This results from the voltage drop across the capacitors multiplied by the respective capacitance . The charge Q on the capacitor is equal to the voltage U on the capacitor. ${\displaystyle Q=C\cdot U}$

calculation

Divider circuit

From and become the equations ${\displaystyle U_{q}={\frac {Q}{C_{\text{Gesamt}}}}}$ ${\displaystyle U_{m}={\frac {Q}{C_{m}}}}$

${\displaystyle Q=C_{\text{Gesamt}}\cdot U_{q}}$ and ${\displaystyle Q=C_{m}\cdot U_{m}}$

where C _{overall represents} a series connection of two capacitors. It will be according to the equation

${\displaystyle C_{\text{Gesamt}}={\frac {C_{v}\cdot C_{m}}{C_{v}+C_{m}}}}$ calculated.

By equating the two approaches for Q we get:

${\displaystyle C_{\text{Gesamt}}\cdot U_{q}=C_{m}\cdot U_{m}}$

At the end you get the voltage you are looking for

${\displaystyle U_{q}={\frac {U_{m}\cdot C_{m}}{C_{\text{Gesamt}}}}}$

The measuring voltage U _M , which can be read on the measuring device, is calculated

${\displaystyle {\begin{aligned}U_{m}&=U_{q}\cdot C_{\text{Gesamt}}\cdot {\frac {1}{C_{m}}}\\&=U_{q}\cdot {\frac {C_{v}\cdot C_{m}}{C_{v}+C_{m}}}\cdot {\frac {1}{C_{m}}}\\&=U_{q}\cdot {\frac {C_{v}}{C_{v}+C_{m}}}\end{aligned}}}$

application

Capacitive voltage dividers are used to measure AC voltage:

• in medium and high voltage systems of the power grid as an alternative to inductive voltage converters
• there for test purposes and to determine the absence of voltage
• as frequency compensation in (high-voltage) test probes ( voltage probes ) Oscilloscopes
• in high-voltage laboratories up to the MV range for voltage measurement even at higher frequencies

Often capacitive voltage dividers have to be damped for measurement purposes in order to avoid resonances with the parasitic circuit elements (inductively acting supply lines). Resistors are assigned to each capacitor if necessary. A voltage divider made of resistors and frequency-compensated by means of a capacitive voltage divider can be used for any type of voltage.

literature

• Andreas Küchler: High voltage technology. Basics - Technology - Applications . 2nd Edition. Springer, 2004, ISBN 3-540-21411-9 .

Individual evidence

1. ↑ Measurement and testing technology II. ( Memento from March 3, 2016 in the Internet Archive ) Slide 17.