**Subject :**Microwave Engineering

## Q Factor of a microstrip line

Many microwave integrated circuits require very high quality resonant circuits. The quality factor Q of a micros trip line is very high, but it is limited by the radiation losses of the substrates and with low dielectric constant. Recall that for uniform current distribution in the microstrip line, the ohmic attenuation constant of a wide microstrip line is given as:

and that the characteristic impedance of a wide microstrip line, as shown

The wavelength in the microstrip line is

where Iis the frequency in GHz

Since Qc is related to the conductor attenuation constant by

where αc is in dB/ Ag , Qc of a wide microstrip line is expressed as

where h is measured in cm and R, is expressed as

Finally, the quality factor Qc of a wide microstrip line is

where α is the conductivity of the dielectric substrate board in Ω/m

For a copper strip

a quality factor Qd is related to the dielectric attenuation constant

From above equations , we can write

where λo is the free-space wavelength in cm. Note that the Qd for the dielectric attenuation constant of a microstrip line is approximately the reciprocal of the dielectric loss tangent θ and is relatively constant with frequency.