In many textbooks, they mentioned that at the microwave frequencies, voltage and current will be different at different points. What is the exact reason? Is there any standard text book or material which has explained these concepts?
Voltage and current in higher frequencies of the total capacitance and inductance is dependent on that frequency, even the tools you use to measure with have inductance and capacitance. You would need to design a measuring instrument specific to the frequency you wish to measure of its voltage and current.
because in high frequency the position of prob measure it's very important and any shift of position you can measure any think (variation of RF signal) . for this reason you can measure Scarting parameter (S) this is sqrt of puissance.
Voltage and current in higher frequencies of the total capacitance and inductance is dependent on that frequency, even the tools you use to measure with have inductance and capacitance. You would need to design a measuring instrument specific to the frequency you wish to measure of its voltage and current.
Thank you Stanley Edwin sir, Very nice Physical explanation
Voltage and current in microwave are equivalent function that contribute to give a electromagnetiv field on the fixed plane of the space. Therefore they are dependent of position, frequency, etc.. I suggest this book 'Foundations for microwave engineering by Robert E. Collin' for explained these concept.
When the system you are considering has a non-trivial solution of the Laplace equation, the E and H fields can be uniquely represented by voltages and currents (down to an additive constant). Example: coaxial transmission line.
When the system has no such solution the voltages and currents are no longer unique representations of the fields. Example: hollow waveguides and resonators.
As mentioned by Pasquale, the Collin books explain this very well.
At microwave frequencies, line parameters are distributed type. The values of element are also distributive throughout the line. The parameter values at the microwave frequencies are very small i.e. inductance of the order of nano Henry and capacitance of pico-farads. We measured voltage at high frequency then lead used to measure voltage will offer a high value of inductance and capacitance which will goes parallel or in series with system impedance. Thus overall impedance of the system will be change. The values measured will be wrong and circuit will not work at microwave frequency because the resonance frequency of any resonant circuit is given by one by two pi under root LC.
Simply speaking it is because the wavelength of the signals is comparable to the line length. Hence at a different point along the line voltage and current is of a different value. Just plot a sinusoidal signal along the line of length equal to one lambda....
The resonant frequency of any resonance Circuit is calculated by a well known formula i.e. 1 by 2 pi under root LC. Thus at microwave frequencies the values of L &C are very small an order of pico ferad & nano henary. When we want to measure voltage and current by using measuring instruments then we need to connect them using leads. Inductance and capacitance of these leads will be an order of farad and henaries and it will goes parallel or series of the system impedance. Consequently the value of overall system will changed to higher values it means now system will resonate at lower frequency. It means we will not get correct values of voltage and current at microwave frequencies. That the reason even we don't use leads at these frequencies.
All thing is very difficult measured in GHz frequency rsrsrs. Basically, due the variations are fast and the wavelength is small to "see" all characteristic of the devices. Then the value is more precisely in terms amplitude and phase. (Pozar)
At microwave frequencies the parameters are distributed, they are a function of frequency and position, hence difficult to measure. Agreed with Stanley Edwin , Pasquale Dottorato and A. K Gautam sir. Thanks for sharing
At the lower frequencies the parameters have lumped nature and at the higher frequencies they have distributed nature. The distributed parameters are function of frequencies and hence voltage and current are not measurable irrespective of frequency of operation of concerned device.
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