4) Microwave dielectric ceramics for resonators and antennas

Microwave dielectric resonators

discs of dielectric that resonate specific frequencies of light; dielectric-air interface reflects EM radiation so certain wavelengths will form a standing wave and resonate increasing the signal strength to be passed on to the amplifier etc, all the other frequencies die out; smaller dielectric = higher frequency

Why is the mounting important for a resonator

the E and B fields are not fully confined and leak slightly into the surrounding air; nearby metal or dielectrics can perturb the resonant frequency

Equation for resonant frequency

f_0 = c/Dsqrt(ε_r)

Why might f_0 vary with temperature

dielectric constant changes with temperature and thermal expansion can change the diameter D which will change f_0

Equation for the temperature coefficient of frequency

TC_f = -1/2(TC_C + α_L)

Why use TC_C instead of TC_ε

TC_C is much easier to measure

Why do we want TC_f = 0

so the frequency remains constant over a large temperature range (-50-80C); preferable tunable to account for changes in surrounding circuit; +-1M/K is often acceptable

Define the Q factor

Q = f_0 / Δf ~1/tanδ; often expressed as a value at f_0=1GHz; at higher frequencies quote Qf_0 (Q x freq in GHz) which is approx constant and comparable to the value measured at 1GHz

How is Δf recorded

3dB below the peak

Trade off between Q and ε_r

materials with high ε usually have low Q (and vice versa) as properties that make dipoles easy to polarise (soft bonds, heavy ions, easily displaced charge centres) also means those dipoles have large inertia and interact with the lattice strongly and therefore have low Q

How is Q affected by complex perovskites

large spread of tolerance factors or bond lengths strongly affects Δf causing low Q due to anharmonic lattice vibrations

How are microwave measurements made

dielectric cylinder placed in metal cavity and two antennae radiate into and extract power from the cavity; ε_r is determine from f_0 and Q from f_0/Δf; TC_f requires measurements at different temperatures; not very accurate (particularly as Q is only measured to within +-10%)