Plot impedances in rectangular form, convert to polar, and read phasor diagrams and the E5-1 figure.
Syllabus: Coordinate systems and phasors in electronics: rectangular coordinates; polar coordinates; phasors; logarithmic axes
Compendium articles on the ideas in this lesson, beyond what the exam asks.
Practise the 12 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".
An impedance is a point on a plane. R goes on the horizontal axis, X on the vertical. Inductive reactance is +j (up), capacitive is −j (down).
| Notation | Means |
|---|---|
| 100 + j0 | pure resistance, on the horizontal axis |
| 0 + j100 | pure inductive reactance |
| 0 − j100 | pure capacitive reactance of 100 Ω |
| 50 − j25 | 50 Ω resistance in series with 25 Ω capacitive reactance |
RememberGraph X axis = resistance. Graph Y axis = reactance. First number is R, the j part is X.
The same point can be given as magnitude and phase angle instead of R and X. Polar form is the natural way to show phase angle.
|Z| = √(R² + X²), θ = arctan(X ÷ R)RememberPure inductive reactance: +90°. Pure capacitive: −90°. Pure resistance: 0°.
Series R and a part at frequency f: compute X, write R ± jX, find the point. The official figure is shown with the question; here are its eight points.
| Circuit | Reactance | Z | Point |
|---|---|---|---|
| 400 Ω + 38 pF at 14 MHz | XC = 1 ÷ (2π × 14×10⁶ × 38×10⁻¹²) = 299 Ω | 400 − j299 | 4 (400, −300) |
| 300 Ω + 18 µH at 3.505 MHz | XL = 2π × 3.505×10⁶ × 18×10⁻⁶ = 396 Ω | 300 + j396 | 3 (300, +400) |
| 300 Ω + 19 pF at 21.2 MHz | XC = 1 ÷ (2π × 21.2×10⁶ × 19×10⁻¹²) = 395 Ω | 300 − j395 | 1 (300, −400) |
RememberCapacitor: below the axis. Inductor: above. R sets how far right.
A phasor is an arrow with a length (size) and an angle (timing). Draw voltage and current phasors together and the angle between them is the phase relationship. Arrows turn counter-clockwise: the one ahead leads.
RememberPhasor diagram = phase relationships at one frequency.
A filter passes some signals and blocks others by factors of thousands. A logarithmic Y axis gives each factor of ten equal height, so both the passband and the deep rejection stay readable.
RememberFrequency-response graphs: logarithmic Y axis (usually dB).