An Introduction to Microwave Measurements by Ananjan Basu

By Ananjan Basu

"This e-book begins with a quick assessment, after which supplies a brief precis of the elemental thought and the construction blocks required to appreciate and use microwave size ideas. After a short description of older dimension concepts (slotted wave consultant etc.) the ebook supplies a pretty distinct description of the vector community analyzer and the spectrum analyzer, which shape the spine of contemporary microwave Read more...

summary: "This booklet starts off with a quick assessment, after which supplies a brief precis of the elemental thought and the construction blocks required to appreciate and use microwave size innovations. After a short description of older size options (slotted wave consultant etc.) the booklet provides a reasonably distinct description of the vector community analyzer and the spectrum analyzer, which shape the spine of recent microwave measurements. complicated themes resembling pulsed measurements and non-linear community research are just pointed out in passing"

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The number of harmonics M should ideally be infinite, but when considering a modulated signal like m(t)cos(2πf0t), M is limited so that Mfm << f0. These keep the expressions simple and also agree with waveforms used in practice. Also, for T1 = T2 (50% duty cycle) the even harmonics are all 0. 15 Autocorrelation of v(t) for <50% duty cycle. T2 Tm τ 32 An Introduction to Microwave Measurements Taking the Fourier transforms, we get the power spectral density of v(t): M Sv ( f ) = 1 Ciδ( f − if m ) R i=− M ∑ There is another way to look at this example: it is easy to expand v(t) in Fourier series: M v(t) = ∑v e i jifmt −M where vi = A πiT1 − jπiT1/Tm e sin Tm πi If we assume that each term contains power |vi|2/R, concentrated at i*f m, expressing this using impulse functions we get the same result for the power spectral density.

So, connecting a resistance R at port 2 will ensure that V2 = – RI2, which in turn will ensure that a2 = 0. A signal source has to be connected a port 1. Let this be a current source I0 (many alternative sources can be used). 7. Let Zm be the impedance seen by the current source. Zm = Zc R + jZc tan βL 10 + j50 tan βL = 50 Zc + jR tan βL 50 + j10 tan βL So, V1 = I0Zm and I1 = I0. S11 can be evaluated from these relations, but for S21 we need V2 and I2 as well. For this, we use the ABCD matrix of the transmission line.

Each column has an additional 0 (other than the diagonal). The magnitude of a nonzero element in any column is either C (the coupling) or T (the through-port transmission or main line loss). The number C (the coupling) is the main specification of the coupler. Usually it is specified in dB: coupling = –20 log10 |C|. To realize the above properties (specially over a broad frequency range) may be a challenging task, especially if the permissible deviation from ideal values is small. Ideally, |C|2 + |T|2 = 1, but in practice there are losses, and |C|2 + |T|2 < 1.

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