Hartley Oscillator Frequency
f = 1 / (2π√((L1+L2) · C))
Quick answer
This calculator solves f = 1 / (2π√((L1 + L2) × C)) for Frequency. With Inductor L1 100 µH, Inductor L2 0.22 mH, Tank Capacitor 100 nF, the result is 28.13 kHz. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The Hartley oscillator is the inductive dual of the Colpitts: its tank uses a tapped inductor (or two inductors in series) with the tap providing feedback, resonating with a single capacitor. The total tank inductance is the sum of the two sections plus any mutual coupling. Hartley circuits are easy to tune with a variable capacitor and were widely used in radio receivers.
Variables
- f — Oscillation frequency (Hz)
- L1 — First inductor section (H)
- L2 — Second inductor section (H)
- C — Tank capacitor (F)
Practical Notes
If the two coil sections are magnetically coupled, add 2M to the total inductance. The L1/L2 ratio sets the feedback fraction needed to sustain oscillation.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | MHz | Hz, kHz, MHz, GHz |
| L1 | Inductor L1 | µH | nH, µH, mH, H |
| L2 | Inductor L2 | µH | nH, µH, mH, H |
| C | Tank Capacitor | nF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Inductor L1 100 µH, Inductor L2 0.22 mH, Tank Capacitor 100 nF
- 2. The relation: f = 1 / (2π√((L1 + L2) × C))
- 3. Substitute: L1 = 100 µH, L2 = 0.22 mH, C = 100 nF
- 4. Result: Frequency = 28.13 kHz
Worked examples
Minimum range
Given: Inductor L1 100 nH, Inductor L2 0.22 µH, Tank Capacitor 100 pF
Result: Frequency = 28.13 MHz
Low range
Given: Inductor L1 1 µH, Inductor L2 2.2 µH, Tank Capacitor 1 nF
Result: Frequency = 2.813 MHz
Typical
Given: Inductor L1 100 µH, Inductor L2 0.22 mH, Tank Capacitor 100 nF
Result: Frequency = 28.13 kHz
High range
Given: Inductor L1 0.47 mH, Inductor L2 1.03 mH, Tank Capacitor 1 µF
Result: Frequency = 4.109 kHz
Maximum range
Given: Inductor L1 4.7 mH, Inductor L2 10.3 mH, Tank Capacitor 10 µF
Result: Frequency = 0.4109 kHz
Solving for each variable
Solve for Frequency
Inductor L1 100 nH, Inductor L2 0.22 µH, Tank Capacitor 100 pF → 28.13 MHz
Solve for Tank Capacitor
Frequency 100 kHz, Inductor L1 100 nH, Inductor L2 0.22 µH → 7.916 µF
Solve for Inductor L1
Frequency 100 kHz, Inductor L2 0.22 µH, Tank Capacitor 100 pF → 25.33 mH
Solve for Inductor L2
Frequency 100 kHz, Inductor L1 100 nH, Tank Capacitor 100 pF → 25.33 mH
How Frequency changes with Inductor L1
| Inductor L1 (input) | Frequency (result) |
|---|---|
| 10 µH | 33.19 kHz |
| 25 µH | 32.15 kHz |
| 50 µH | 30.63 kHz |
| 75 µH | 29.3 kHz |
| 100 µH | 28.13 kHz |
| 150 µH | 26.16 kHz |
| 0.2 mH | 24.56 kHz |
| 0.4 mH | 20.21 kHz |
| 0.7 mH | 16.59 kHz |
| 1 mH | 14.41 kHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 28130 |
| kHz | 28.13 |
| MHz | 0.02813 |
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<p><a href="https://vbatpower.com/formulas/hartley-oscillator/">Hartley Oscillator Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Hartley Oscillator Frequency?
Use f = 1 / (2π√((L1 + L2) × C)). With Inductor L1 100 µH, Inductor L2 0.22 mH, Tank Capacitor 100 nF, Frequency works out to 28.13 kHz.
What is the formula for Hartley Oscillator Frequency?
The formula is f = 1 / (2π√((L1 + L2) × C)). The Hartley oscillator is the inductive dual of the Colpitts: its tank uses a tapped inductor (or two inductors in series) with the tap providing feedback, resonating with a single capacitor.
How do you find Tank Capacitor when you know the other values?
Rearrange for Tank Capacitor: with Frequency 100 kHz, Inductor L1 100 nH, Inductor L2 0.22 µH, Tank Capacitor is 7.916 µF.
How do you find Inductor L1 when you know the other values?
Rearrange for Inductor L1: with Frequency 100 kHz, Inductor L2 0.22 µH, Tank Capacitor 100 pF, Inductor L1 is 25.33 mH.
What units does Hartley Oscillator Frequency use?
Frequency is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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