Varactor Diode Capacitance
C = Cj0 / (1 + V/Vbi)^m
Quick answer
This calculator solves C = C_j0 / (1 + V/V_bi)^m for C. With Zero-Bias Capacitance 100 pF, Reverse Bias Voltage 12 V, Built-in Potential 26.4 V, Grading Coefficient 0.5, the result is 8.29 × 10⁻¹¹.
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Formula
Description
A varactor (varicap) diode has a junction capacitance that varies with the applied reverse bias voltage. As reverse voltage increases, the depletion region widens, reducing capacitance. Cj0 is the zero-bias junction capacitance, Vbi is the built-in junction potential (about 0.7 V for silicon), and m is the grading coefficient (0.5 for an abrupt junction, 0.33 for a linearly graded junction, up to 2 for hyperabrupt varactors). Varactors are used in voltage-controlled oscillators (VCOs), phase-locked loops (PLLs), and frequency synthesizers.
Variables
- C_j0 — Zero-bias junction capacitance (F)
- V — Applied reverse bias voltage (V, positive value)
- V_bi — Built-in junction potential (V, typically 0.6-0.8 for Si)
- m — Grading coefficient (0.3-2, dimensionless)
Practical Notes
Hyperabrupt varactors (m ≈ 1-2) provide a more linear frequency vs. voltage characteristic in VCO applications. Typical tuning ratios: abrupt junction 3:1, hyperabrupt 10:1 or more. The Q factor of varactors decreases at higher frequencies due to series resistance. For best Q, use the lowest reverse voltage that achieves the desired capacitance. All pn junction diodes exhibit this effect; varactors are simply optimized for it.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Cj0 | Zero-Bias Capacitance | pF | pF, nF, µF, mF, F |
| V | Reverse Bias Voltage | V | pV, nV, µV, mV, V, kV |
| Vbi | Built-in Potential | V | pV, nV, µV, mV, V, kV |
| m | Grading Coefficient | — | — |
Step by step
- 1. What you know: Zero-Bias Capacitance 100 pF, Reverse Bias Voltage 12 V, Built-in Potential 26.4 V, Grading Coefficient 0.5
- 2. The relation: C = C_j0 / (1 + V/V_bi)^m
- 3. Substitute: Cj0 = 100 pF, V = 12 V, Vbi = 26.4 V, m = 0.5
- 4. Result: C = 8.29 × 10⁻¹¹
Worked examples
Minimum range
Given: Zero-Bias Capacitance 1 pF, Reverse Bias Voltage 0.33 V, Built-in Potential 0.726 V, Grading Coefficient 0.025
Result: C = 9.91 × 10⁻¹³
Low range
Given: Zero-Bias Capacitance 10 pF, Reverse Bias Voltage 3.3 V, Built-in Potential 7.26 V, Grading Coefficient 0.25
Result: C = 9.11 × 10⁻¹²
Typical
Given: Zero-Bias Capacitance 100 pF, Reverse Bias Voltage 12 V, Built-in Potential 26.4 V, Grading Coefficient 0.5
Result: C = 8.29 × 10⁻¹¹
High range
Given: Zero-Bias Capacitance 1 nF, Reverse Bias Voltage 0.23 kV, Built-in Potential 0.506 kV, Grading Coefficient 0.8
Result: C = 7.41 × 10⁻¹⁰
Maximum range
Given: Zero-Bias Capacitance 10 nF, Reverse Bias Voltage 2.3 kV, Built-in Potential 5.06 kV, Grading Coefficient 8
Result: C = 4.99 × 10⁻¹⁰
How C changes with Zero-Bias Capacitance
| Zero-Bias Capacitance (input) | C (result) |
|---|---|
| 10 pF | 8.29 × 10⁻¹² |
| 25 pF | 2.07 × 10⁻¹¹ |
| 50 pF | 4.15 × 10⁻¹¹ |
| 75 pF | 6.22 × 10⁻¹¹ |
| 100 pF | 8.29 × 10⁻¹¹ |
| 150 pF | 1.24 × 10⁻¹⁰ |
| 0.2 nF | 1.66 × 10⁻¹⁰ |
| 0.4 nF | 3.32 × 10⁻¹⁰ |
| 0.7 nF | 5.8 × 10⁻¹⁰ |
| 1 nF | 8.29 × 10⁻¹⁰ |
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<p><a href="https://vbatpower.com/formulas/varactor-capacitance/">Varactor Diode Capacitance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Varactor Diode Capacitance?
Use C = C_j0 / (1 + V/V_bi)^m. With Zero-Bias Capacitance 100 pF, Reverse Bias Voltage 12 V, Built-in Potential 26.4 V, Grading Coefficient 0.5, C works out to 8.29 × 10⁻¹¹.
What is the formula for Varactor Diode Capacitance?
The formula is C = C_j0 / (1 + V/V_bi)^m. A varactor (varicap) diode has a junction capacitance that varies with the applied reverse bias voltage.
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