Calculate RC Differentiator

Calculator and formulas for calculating an RC differentiator circuit

Calculate Differentiator

RC Differentiator Circuit

This function can calculate the properties of an RC differentiator circuit. The function calculates the capacitor, resistor, or period/frequency.

Results
Resistor:
Capacitor:
Frequency:
Period:

Differentiator Circuit

Pulse Shaping Stage

The differentiator functions as a pulse shaping stage. The CR circuit generates a pulse-like AC voltage at the output from a square wave voltage at the input.

Square wave pulse
T = Period, t1 = Pulse
RC Differentiator Circuit
Time Constant τ (tau)

The time constant of an RC circuit is the product of R · C. The unit is seconds. The symbol is the Greek letter τ (tau).

After 5τ, the charge is approximately 99.3%.

RC Differentiator - Theory and Formulas

How the Differentiator Works

The differentiator functions as a pulse shaping stage. The CR circuit generates a pulse-like AC voltage at the output from a square wave voltage at the input.

Pulse Shapes with Different Time Constants

t1 = 5τ Optimal Differentiation
5 tau pulse shape
\[t1 = 5 \cdot R \cdot C\] \[R = \frac{t1}{5 \cdot C}\] \[C = \frac{t1}{5 \cdot R}\]

When the length of the square wave pulse (t1) equals 5 times the time constant τ, an optimal pulse sequence is created.

t1 = 10τ Short Pulses
10 tau pulse shape
\[t1 = 10 \cdot R \cdot C\] \[R = \frac{t1}{10 \cdot C}\] \[C = \frac{t1}{10 \cdot R}\]

When the pulse duration is much greater than 5τ, short pulses equal to the input voltage amplitude are generated.

Time Constant and Charging Behavior

The Time Constant τ (tau)
\[\tau = R \times C\]
  • The time constant is the product of R × C
  • Unit: Seconds (s)
  • Symbol: τ (Greek letter tau)
  • After 5τ, the charge is approximately 99.3%
  • Determines the speed of charge/discharge processes

Practical Applications

Signal Processing:
• Edge detectors
• Pulse shapers
• Trigger circuits
• Spike generators
Digital Technology:
• Clock pulse generators
• Reset pulses
• Synchronization
• Timing circuits
Measurement Technology:
• Frequency measurement
• Clock derivation
• Calibration pulses
• Reference signals

Design Guidelines

Optimal Dimensioning
  • For clean differentiation: t1 ≥ 5τ
  • For short pulses: t1 ≥ 10τ
  • Output amplitude: Approximately equal to input amplitude
  • Pulse width: Dependent on time constant
  • Loading: High input impedance of following amplifier
  • Frequency range: Dependent on τ and desired pulse shape

Mathematical Relationships

Basic Formulas
\[\tau = R \times C\] \[t1 = n \times \tau\]

Where n is the factor (typically 5 or 10)

Conversions
\[R = \frac{t1}{n \times C}\] \[C = \frac{t1}{n \times R}\]

Calculation of components for given t1

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Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •