# [Schering Bridge Calculator](https://blog.hirnschall.net/tools/schering-bridge/) author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/) meta description: Calculate unknown capacitance and ESR from a balanced Schering bridge. Enter C2, R3, R4, C4 at null; C_x, R_x, dissipation factor, and loss angle are computed. meta title: Schering Bridge Calculator — Capacitance, ESR, and Dissipation Factor date published: 11.05.2026 (DD.MM.YYYY format) date last modified: 11.05.2026 (DD.MM.YYYY format) --- Calculator ---------- Enter the four bridge components at balance. The unknown capacitance \( C\_x \) and its series resistance \( R\_x \) (ESR) are calculated from the balance conditions. Providing the test frequency also yields the dissipation factor \( D \) and quality factor \( Q \). * C2 (standard capacitor): * µF nF pF * R3 (ratio arm): * Ω kΩ MΩ * R4 (standard arm, variable): * Ω kΩ MΩ * C4 (standard arm, parallel with R4): * µF nF pF --- * Test frequency (f) — optional: * Hz kHz Enter all four bridge components to calculate. Calculate Schering Bridge — Explanation ----------------------------- The Schering bridge is an AC bridge circuit used to measure the capacitance and loss of an unknown capacitor. It places the unknown capacitor \( C\_x \) with its equivalent series resistance \( R\_x \) (ESR) in one arm, balances it against a lossless standard capacitor \( C\_2 \) in the adjacent arm, and reads off \( C\_x \) and \( R\_x \) from the values of the other two bridge components at null. It is widely used in high-voltage testing of cables, bushings, and insulating materials, where the dissipation factor is a key indicator of dielectric quality. The bridge has four arms. The unknown arm contains \( C\_x \) in series with \( R\_x \). The opposite arm contains the standard capacitor \( C\_2 \), which is assumed lossless. The two remaining arms are \( R\_3 \) (a ratio resistor) and the standard arm \( R\_4 \) in parallel with \( C\_4 \). An AC source drives one diagonal; a null detector monitors the other. Balance Conditions ------------------ Setting the complex impedance products of opposite arm pairs equal and separating real and imaginary parts gives: \[ C\_x = C\_2 \cdot \frac{R\_4}{R\_3} \] \[ R\_x = R\_3 \cdot \frac{C\_4}{C\_2} \] Like the Maxwell bridge, these conditions are independent of frequency — the source frequency does not need to be known precisely to measure \( C\_x \) and \( R\_x \). The dissipation factor, however, does depend on frequency: \[ D = \tan\delta = \omega C\_x R\_x = \omega R\_4 C\_4 \] where \( \omega = 2\pi f \). \( D \) can be read directly from the standard arm components once the bridge is balanced, provided the test frequency is known. The quality factor \( Q = 1/D \) is the inverse of the dissipation factor. For a good-quality capacitor — film, ceramic, or mica types — \( D \) is very small (below 0.01), meaning \( Q \) is large. Electrolytic capacitors have much higher losses, with \( D \) values of 0.05 to 0.2 or more at low frequencies. Dissipation Factor and Loss Angle --------------------------------- The dissipation factor \( D = \tan\delta \) describes the fraction of energy dissipated per cycle relative to the energy stored. The loss angle \( \delta \) is the complement of the phase angle: a perfect capacitor has \( \delta = 0° \) (current leads voltage by exactly 90°); a real capacitor with some ESR has \( \delta > 0° \), meaning the current leads by slightly less than 90°. The relationship is: \[ \delta = \arctan(D) = \arctan(\omega C\_x R\_x) \] In high-voltage insulation testing, \( \tan\delta \) (often written as the power factor for small angles where \( \tan\delta \approx \sin\delta \)) is the primary diagnostic quantity. A rising \( \tan\delta \) over time or with voltage indicates degrading insulation. Purpose of the Calculator ------------------------- In a physical measurement, the bridge is brought to null by adjusting \( R\_4 \) (which controls the capacitive balance, setting \( C\_x \)) and \( C\_4 \) (which controls the resistive balance, setting \( R\_x \) and \( D \)). Once the detector reads zero, those component values are entered here to recover \( C\_x \), \( R\_x \), \( D \), \( Q \), and \( \delta \). Frequency is only required for the dissipation factor and loss angle; \( C\_x \) and \( R\_x \) come from the component ratios alone. For component selection, the formulas rearrange to: \( R\_3 = C\_2 R\_4 / C\_x \) and \( C\_4 = C\_2 R\_x / R\_3 \). Choosing \( C\_2 \) and \( R\_3 \) to match the expected range of \( C\_x \) keeps \( R\_4 \) in a convenient adjustment range. Related Tools ------------- * [Maxwell Bridge Calculator](https://blog.hirnschall.net/tools/maxwell-bridge/) — the inductive equivalent: measures unknown inductance and series resistance. * [Wheatstone Bridge Calculator](https://blog.hirnschall.net/tools/wheatstone-bridge/) — DC bridge for measuring unknown resistance. * [Capacitor Impedance Calculator](https://blog.hirnschall.net/tools/capacitor-impedance/) — compute \( X\_C \) and \( |Z| \) from the measured \( C\_x \) and \( R\_x \). * [Capacitor Energy Calculator](https://blog.hirnschall.net/tools/capacitor-stored-energy/) — compute the energy stored in the measured capacitor at a given voltage. More calculators: [blog.hirnschall.net/tools/](https://blog.hirnschall.net/tools/).