Lumped Element Matching

• Find intersection of SWR = 1 and SWR circle
• Finbd value that cancels the imaginary part
• Inductive loads → match with capacitor in parallel
• Capacitive loads → match with inductor in parallel
• Cancel the real part of the
• To solve for the value of L or C:
  • Denormalize (multiply by $z_0$ for $z$, divide by $z_0$ for $y$)
  • Equate to $Z_L$ or $Z_C$ and solve for L/C

Double-stub matching

Single-stub matching

• Find distance at which reactance (imaginary part) cancels
  • This is the distance from the load
• Find $h$, this is the stub length
  • STOP - START
  • START = OC/YC
  • END = stub

Maxwell’s Equations

Gauss’ Law for Electric Fields: relates electric flux density $D$ and electric charge density $\rho _v$

$$ \nabla \cdot \mathbf{D} = \rho_v \newline \oint_S \mathbf{D} \cdot d\mathbf{s} = Q_{enc}

$$

Gauss’ Law for Magnetic Fields: no magnetic monopoles, so magnetic flux density $B$ has no divergence

$$ \nabla \cdot \mathbf{B} = 0 \newline \oint_S \mathbf{B} \cdot d\mathbf{s} = 0

$$

Faraday’s Law of Induction: relates a time-varying magnetic field to an induced electric field

$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \newline \oint_C \mathbf{E} \cdot d\mathbf{l} = -\int_S \frac{\partial \mathbf{B}}{\partial t} \cdot d\mathbf{s}

$$

Ampere’s Law: relates magnetic fields to currents and time-varying electric fields