Reaney- Resonators and Antennas

Question 1

What are microwave dielectric resonators used for?

Answer 1

Present in most telecommunication systems. Generally present to act as filters and resonators for microwave radiation over a large range of frequencies from 400MHz to 13GHz.

Question 2

Principle of operation for resonators

Answer 2

Ability of the dielectric/air interface to reflect EM radiation and give the possibility that the material can sustain a standing EM wave within its body

Question 3

How does resonator generally work with analogy

Answer 3

The body when irradiated with the correct frequency can be at resonance acting as a filter. Analogy for standing waves is blowing imparts on woodwind instrument sound of many frequencies. One of which is the resonant frequency of the required note. Nature of standing wave for MW complicated by fact that EM radiation has magnetic and electric field

Question 4

Formula for resonant frequency

Answer 4

f0=c/λ0
c is velocity of wave in free space
λ0 is wavelength of wave in free space
Or
f0=c/(λdεr^1/2)=c/(Dεr^1/2)

Question 5

Velocity of wave in non-magnetic medium

Answer 5

vd=c/εr^1/2
εr^1/2 would be the refractive index at higher optical frequencies
Now it’s the permittivity

Question 6

Formula for wavelength of standing wave

Answer 6

λd=λ0/εr^1/2

Also approximates to D (diameter of sample)

Question 7

Why may the resonant frequency temperature dependent?

Answer 7

Dielectric constant changes with temperature (as in BaTiO3) and D changes with temperature as a function of the thermal expansion coefficient.

Question 8

Temperature coefficient of resonant frequency

Answer 8

TCf=-1/2TCε-αL
Also TCc=TCε+αL
So TCf=-1/2(TCc+αL)
Where f, ε, L and c are subscript
TCε is temperature coefficient of dielectric constant
TCc is temperature coefficient of capacitance
α sub L is thermal expansion coefficient

Question 9

How can resonating frequency be made temperature independent?

Answer 9

If we balance TCc+αL so the result is close to 0. Preferably tuneable with composition and processing so changes in surrounding circuit can be accounted for. A range of +/- 1MK^-1 is acceptable for most design requirements. This unit is equivalent to ppm/°C

Question 10

What is the quality factor of a microwave dielectric?

Answer 10

Q. Given by f0/Δf and under conditions where the energy loss is confined to the dielectric. Is also approximately given by the reciprocal of the dielectric loss tanδ. This value of tanδ is that at microwave resonance and not that found durning conventional measurements at low frequencies. Larger Q is better filter

Question 11

Where is Δf taken at?

Answer 11

At 3dB below the peak height of the relative transmitted power vs frequency graph

Question 12

What is true for a poor resonator?

Answer 12

Relative transmitted power is low, peak height is low, Δf/f0 is large so Q small. Means selectivity of filter is poor.

Question 13

Graph of relative transmitted power/dB vs frequency

Answer 13

Starts low until near f0 where rapidly rises to peak then comes down similarly the other side of f0

Question 14

Trade off between Q and εr

Answer 14

Materials with high εr usually have low Q and vice versa.

Question 15

Why do solid solutions and complex perovskites have low Q?

Answer 15

The spread of tolerance factors (ΔT) or bond lengths strongly affects Qf0 with large spreads resulting in low Q due to anharmonic vibrations within the lattice

Question 16

How is Q commonly expressed?

Answer 16

As a value obtained at an f0 of 1GHz. When values are obtained at higher frequencies, value of Qf0 is quoted which is approximately constant and comparable with the value measured at 1GHz.

Question 17

Experiment set up and data recorded for microwave measurement

Answer 17

Dielectric cylinder placed inside a metal cavity. Two antennae radiate into and extract power from the cavity. They are only loosely coupled electromagnetically to the resonant system. εr determined from f0 and Q from f0/Δf. TCf requires these measurements to be made as a function of temperature. Accuracy not high particularly as Q only measured to +/-10%

Question 18

Modern microwave dielectric ceramics for resonators

Answer 18

See table on slide 21

Question 19

What are geo stationary satellites used for?

Answer 19

To give accurate position and time to mobile handsets such as in satellite navigation systems and in smart phones.

Question 20

What type of radiation do satellites emit?

Answer 20

Circularly polarised rather than linearly polarised radiation. Shared like a spring

Question 21

What are dielectrically loaded antennas composed of?

Answer 21

Ceramic substrates upon which metallisations are deposited. Resonators don’t use metallisation within a conventional cavity.

Question 22

What does presence of metallisations for antennas mean?

Answer 22

That the dielectric loss of ceramic is not as critical as in resonators. TCf can also be up to 10MK^-1 rather than 1MK^1. However is now strong drive towards miniaturisation and therefore higher εr.

Question 23

Most important metrics for antenna

Answer 23

The efficiency (ratio of strength of signal to the resonance) often 25-50%.
Radiation pattern which must be good in elevation as well as out towards the horizon (azimuth).
Antenna must be sensitive to right hand as opposed to left hand circular polarisation so that reflections in urban areas don’t give false positional readings