kicad/pcb_calculator/attenuators/pi_formula.html

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<p style="margin-bottom: 0cm; font-style: normal; font-weight: normal; line-height: 100%">
<font face="Times New Roman, serif"><font size="6" style="font-size: 22pt"><b>Z</b><sub><b>in</b></sub>
desired input impedance in &#8486;</font></font></p>
<p style="margin-bottom: 0cm; font-style: normal; font-weight: normal; line-height: 100%">
<font face="Times New Roman, serif"><font size="6" style="font-size: 22pt"><b>Z</b><sub><b>out</b></sub><sub>
</sub> desired output impedance in &#8486;</font></font></p>
<p style="margin-bottom: 0cm; font-style: normal; font-weight: normal; line-height: 100%">
<font face="Times New Roman, serif"><font size="6" style="font-size: 22pt">a
attenuation in dB</font></font></p>
<p style="margin-bottom: 0cm; font-style: normal; font-weight: normal; line-height: 100%">
<font face="Times New Roman, serif"><font size="6" style="font-size: 22pt">L
= 10<sup>a/10</sup> (the loss)</font></font></p>
<p style="margin-bottom: 0cm; font-style: normal; font-weight: normal; line-height: 100%">
<font face="Times New Roman, serif"><font size="6" style="font-size: 22pt">A
= (L + 1)/(L &minus; 1)</font></font></p>
<p style="margin-bottom: 0cm; font-style: normal; font-weight: normal; line-height: 100%">
<br/>
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<p style="margin-bottom: 0cm; font-style: normal; line-height: 100%"><font face="Times New Roman, serif"><font size="6" style="font-size: 28pt"><b>Pi
attenuator</b></font></font></p>
<p style="margin-bottom: 0cm; line-height: 100%"><font face="Times New Roman, serif"><font size="6" style="font-size: 28pt"><i><b>R2
= (L &minus; 1)/2 * &radic; ((Z<sub>in</sub> * Z<sub>out</sub>)/L)</b></i></font></font></p>
<p style="margin-bottom: 0cm; line-height: 100%"><font face="Times New Roman, serif"><font size="6" style="font-size: 28pt"><i><b>R1
= 1/( A/Z<sub>in</sub> &minus; 1/R2)</b></i></font></font></p>
<p style="margin-bottom: 0cm; line-height: 100%"><font face="Times New Roman, serif"><font size="6" style="font-size: 28pt"><i><b>R3
= 1/ (A/Z<sub>out</sub> &minus; 1/R2)</b></i></font></font></p>
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