Wideband Filters
- Thread starter Antonio
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Certainly. Consider a voltage source with some internal resistance, called small r. Consider an external load resistance called big R. Question, for any voltage V and internal resistance small r, when will the maximum power be transferred to the load resistor big R? The answer is, when small r equals big R.
Simple right? Now replace small r and big R with impedances small z and Big Z which are frequency dependent. Question, for any AC voltage source V=Ae^(jωt) and source impedance small z, when will the maximum power be transferred to the load impedance big Z?.
If you said when small z is equal to Big Z....AANNNGH! loose 2 points. This is complex algebra here. The correct answer is when Big Z is equal to the complex conjugate of small z. This is called a "complex conjugate match" or sometimes just a "conjugate match".
Inductors have impedances with positve imaginary parts whose value is
ωL, a linear function of frequency. Capacitors have impedances with negative imaginary parts whose value is (ωC)^-1 which is NOT a linear function of frequency. Over a narrow range of frequencies it is possible to do a conjugate match. Over a wide band it becomes increasingly difficult as the bandwidth increases.
At RF frequencies a small return loss corresponds precisely to power being delivered to the load. A big return loss corresponds to power being reflected from the load and returning to the source. 25 dB down is a pretty good return loss, 3 dB down is a not so good return loss.
Simple right? Now replace small r and big R with impedances small z and Big Z which are frequency dependent. Question, for any AC voltage source V=Ae^(jωt) and source impedance small z, when will the maximum power be transferred to the load impedance big Z?.
If you said when small z is equal to Big Z....AANNNGH! loose 2 points. This is complex algebra here. The correct answer is when Big Z is equal to the complex conjugate of small z. This is called a "complex conjugate match" or sometimes just a "conjugate match".
Inductors have impedances with positve imaginary parts whose value is
ωL, a linear function of frequency. Capacitors have impedances with negative imaginary parts whose value is (ωC)^-1 which is NOT a linear function of frequency. Over a narrow range of frequencies it is possible to do a conjugate match. Over a wide band it becomes increasingly difficult as the bandwidth increases.
At RF frequencies a small return loss corresponds precisely to power being delivered to the load. A big return loss corresponds to power being reflected from the load and returning to the source. 25 dB down is a pretty good return loss, 3 dB down is a not so good return loss.
