Question 1:
A complex load impedance (ZL) of value 80Ω – j65Ω, is connected at the far (distal) end of a co-axial transmission line with a characteristic impedance (Z0) of 50? and a PTFE dielectric, with a dielectric constant of 1.3, is used to separate the two conductors. It is assumed that the dielectric material is homogenous and the geometry of the coaxial cable does not vary along the length of the line. Assuming energy at a single frequency of 10GHz is to be used as a carrier to transmit data, calculate the following:
a. Impedance (Zin), magnitude and phase of reflection coefficient (Γ), voltage standing wave ratio (VSWR) and return loss (RL) at a distance of 15cm away from the load.
b. Γ, VSWR and RL at the load
c. Comment on this result
Question 2:
A quarter wavelength (λ/4) or odd multiple of quarter wavelength (2n-1)λ/4 long section of lossless co-axial transmission line cable is used to realise an impedance matching transformer. The transformer has a characteristic impedance Z0. It is used to match the energy delivered from a microwave generator, with a source impedance (Zs) of 75?, to a load impedance ZL of (20+j0) ? that represents a biological tissue load at the frequency of interest.
a. What value of Z0 is required to match the source to the load?
b. If the generator operates at a single frequency of 12GHz, and the relative permittivity (εr) of the co-axial cable used to implement the transformer is 2.3, what are the first two physical lengths of co-axial cable that could be used to realise this transformer in practice?
c. Sketch the quarter wavelength transformer, showing ZS, Z0, and ZL
d. Now that the source is matched to the load and any power loss due to the length of co-axial transmission is negligible (for short lengths of low loss transmission line operated at frequencies of less than 18GHz, this is a valid assumption), we can assume that the input power (Pin) will be the same as the power at the load (PL). If Pin is 10W, show the variation of voltage and current along the first quarter wavelength transformer.
Question 3:
A microwave generator is arranged to deliver power at a frequency of 14.5GHz into biological tissue to perform focussed coagulation of blood vessels. An applicator with an effective impedance of 15Ω (this takes into account the impedance of the vessels coupled to the end of the applicator and can be considered to be load impedance ZL) is used to deliver the microwave energy into the vessels. The microwave generator has an input (source) impedance of 50Ω, and a 2.5m lossless 25Ω transmission line is used to connect the output of the generator to the 15Ω effective load impedance (ZL). It is necessary to transfer as much power as possible from the generator to the antenna.
I. Show how you could use two quarter wave transformers (one at each end of the transmission line) to match the power delivered into the effective load ZL
II. Calculate the characteristic impedance and the length of each transformer (assume that co-axial transmission line is used for each transformer and that the relative permittivity of the dielectric material between the inner and outer conductors is 1.6 in each case)