Reactance, phase, impedance and coupling
Phase in inductors and capacitors, calculating reactance, capacitors for coupling and decoupling, RF chokes, and impedance in series CR and LR circuits.
Key points
Summary
| Item | Formula or rule |
|---|---|
| Inductive reactance | XL = 2πfL |
| Capacitive reactance | XC = 1 ÷ 2πfC |
| Phase | L: I lags V · C: I leads V |
| Impedance | Z = √(R² + X²) |
| Current | I = V ÷ Z |
| Coupling / decoupling / choke | Block DC / bypass RF / block RF |
Quick check
In a capacitor, how does the current relate to the voltage?
- It leads by 90°
- It lags by 90°
- It is in phase
- It leads by 180°
What is the reactance of 100 pF at 14 MHz, approximately?
- 8.8 kΩ
- 114 Ω
- 1.14 Ω
- 11.4 kΩ
R = 30 Ω and X = 40 Ω are in series. What is the impedance?
- 70 Ω
- 10 Ω
- 50 Ω
- 1200 Ω
Work it out
Try each one first, then open it to see the working.
Find the reactance of 10 µH at 7 MHz.
- XL = 2πfL = 2π × 7×10⁶ × 10×10⁻⁶
Find the reactance of 100 pF at 14 MHz.
- XC = 1 ÷ (2π × 14×10⁶ × 100×10⁻¹²)
30 Ω and a reactance of 40 Ω are in series across 10 V. Find the current.
- Z = √(30² + 40²) = 50 Ω
- I = 10 ÷ 50
What capacitance has a reactance of 50 Ω at 3.6 MHz?
- C = 1 ÷ (2πf × XC)
- C = 1 ÷ (2π × 3.6×10⁶ × 50)
On air
- Work out the reactance of a 100 nF decoupling capacitor at 7 MHz and at 50 Hz.
- Find the coupling and decoupling capacitors in a circuit diagram of any kit.
- Practise the impedance triangle with 3-4-5 and 5-12-13 values.
Video transcript
Capacitors and inductors resist alternating current in a way that depends on frequency. In this lesson: phase, reactance, coupling and decoupling, and how to combine resistance and reactance into impedance.
Inductive reactance is two pi f L, so it rises in proportion to frequency. Meanwhile capacitive reactance is one divided by two pi f C, so it falls as frequency rises. Both are measured in ohms, using hertz, henries and farads. You can rearrange either formula to find the component value from a reactance, or the frequency at which a part has a given reactance. For example, ten microhenries at seven megahertz has a reactance of about four hundred and forty ohms.
In an inductor, the current lags the voltage by ninety degrees. In a capacitor, the current leads the voltage by ninety degrees. A handy memory aid is the word civil: in C, I comes before V; and V comes before I in L. This phase difference is why you can't simply add resistance and reactance.
A coupling capacitor passes the A C signal from one stage to the next, but blocks the D C, so the stages' bias voltages don't upset each other. A decoupling capacitor goes from a supply line to ground, giving A C and R F signals an easy path to ground so they can't travel along the supply to other stages. An inductor does the opposite job. As an R F choke, it passes the D C supply but blocks the R F signal.
Impedance combines resistance and reactance. Because they're ninety degrees apart, you add them like the sides of a right angled triangle. The impedance is the square root of the resistance squared plus the reactance squared. Then the current is the voltage divided by the impedance. The same applies to voltages: the voltages across the resistor and the reactance add up the same way to give the supply voltage. With thirty ohms of resistance and forty ohms of reactance, the impedance is fifty ohms, and ten volts drives two hundred milliamps.
This is one of 25 lessons in the Full course
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