HW $10$

Design a low$-$pass RC $($no inductors$)$ filter with a cut$-$off frequency of f$\_($c$)=2500$Hz$.$

Remember omega$=2$pi f$.$

Use the tables provide for standard Resistor and Capacitor values $($Next Page$).$

I recommend you choose an appropriate Capacitor then add resistors in parallel and$/$or in

series to get the needed equivalent resistance in the appropriate part of the circuit. You should

try to get your cutoff frequency within $1\%$ of the specified value.

Please include your circuit drawing and how you determined the sizes of the components.

Part $2$

For your circuit, derive the Frequency Response Gain G$\_($v$)($f$)$ in terms of frequency.

Provide your derivation of the frequency response function. Then use Matlab to generate the

Bode Plots. Please provide the appropriate Bode plots that cover a frequency range of $10$ Hz to

$100$ kHz $.$

Please upload this document as a pdf$.$ Include your Matlab $.$m file., Standard Resistors

$\backslash$begin$\{$tabular$\}\{|$r$|$r$|$r$|$r$|$r$|\}$

$\backslash$hline ohm & ohm & ohm & k$-$ohm & k$-$Ohm $\backslash \backslash$

$\backslash$hline $1$ & $10$ & $100$ & $1$ & $10\backslash \backslash$

$\backslash$hline $1\mathrm{.}2$ & $12$ & $120$ & $1\mathrm{.}2$ & $12\backslash \backslash$

$\backslash$hline $1\mathrm{.}5$ & $15$ & $150$ & $1\mathrm{.}5$ & $15\backslash \backslash$

$\backslash$hline $1\mathrm{.}8$ & $18$ & $180$ & $1\mathrm{.}8$ & $18\backslash \backslash$

$\backslash$hline $2\mathrm{.}2$ & $22$ & $220$ & $2\mathrm{.}2$ & $22\backslash \backslash$

$\backslash$hline $2\mathrm{.}7$ & $27$ & $270$ & $2\mathrm{.}7$ & $27\backslash \backslash$

$\backslash$hline $3\mathrm{.}3$ & $33$ & $330$ & $3\mathrm{.}3$ & $33\backslash \backslash$

$\backslash$hline $3\mathrm{.}9$ & $39$ & $390$ & $3\mathrm{.}9$ & $39\backslash \backslash$

$\backslash$hline $4\mathrm{.}7$ & $47$ & $470$ & $4\mathrm{.}7$ & $47\backslash \backslash$

$\backslash$hline $5\mathrm{.}6$ & $56$ & $560$ & $5\mathrm{.}6$ & $56\backslash \backslash$

$\backslash$hline $6\mathrm{.}8$ & $68$ & $680$ & $6\mathrm{.}8$ & $68\backslash \backslash$

$\backslash$hline $8\mathrm{.}9$ & $89$ & $890$ & $8\mathrm{.}9$ & $89\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Standard Capacitors

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline pF & pF & pF & pF & uF & uF & uF & uF & uF & uF $\backslash \backslash$

$\backslash$hline $1$ & $10$ & $100$ & $1000$ & $0\mathrm{.}01$ & $0\mathrm{.}1$ & $1$ & $10$ & $100$ & $1000\backslash \backslash$

$\backslash$hline $1\mathrm{.}1$ & $11$ & $110$ & $1100$ & & & & & & $\backslash \backslash$

$\backslash$hline $1\mathrm{.}2$ & $12$ & $120$ & $1200$ & & & & & & $\backslash \backslash$

$\backslash$hline $1\mathrm{.}3$ & $13$ & $130$ & $1300$ & & & & & & $\backslash \backslash$

$\backslash$hline $1\mathrm{.}5$ & $15$ & $150$ & $1500$ & $0\mathrm{.}015$ & $0\mathrm{.}15$ & $1\mathrm{.}5$ & $15$ & $150$ & $1500\backslash \backslash$

$\backslash$hline $1\mathrm{.}6$ & $16$ & $160$ & $1600$ & & & & & & $\backslash \backslash$

$\backslash$hline $1\mathrm{.}8$ & $18$ & $180$ & $1800$ & & & & & & $\backslash \backslash$

$\backslash$hline $2$ & $20$ & $200$ & $2000$ & & & & & & $\backslash \backslash$

$\backslash$hline $2\mathrm{.}2$ & $22$ & $220$ & $2200$ & $0\mathrm{.}022$ & $0\mathrm{.}22$ & $2\mathrm{.}2$ & $22$ & $220$ & $2200\backslash \backslash$

$\backslash$hline $2\mathrm{.}4$ & $24$ & $240$ & $2400$ & & & & & & $\backslash \backslash$

$\backslash$hline $2\mathrm{.}7$ & $27$ & $270$ & $2700$ & & & & & & $\backslash \backslash$

$\backslash$hline $3$ & $30$ & $300$ & $3000$ & & & & & & $\backslash \backslash$

$\backslash$hline $3\mathrm{.}3$ & $33$ & $330$ & $3300$ & $0\mathrm{.}033$ & $0\mathrm{.}33$ & $3\mathrm{.}3$ & $33$ & $330$ & $3300\backslash \backslash$

$\backslash$hline $3\mathrm{.}6$ & $36$ & $360$ & $3600$ & & & & & & $\backslash \backslash$

$\backslash$hline $3\mathrm{.}9$ & $39$ & $390$ & $3900$ & & & & & & $\backslash \backslash$

$\backslash$hline $4\mathrm{.}3$ & $43$ & $430$ & $4300$ & & & & & & $\backslash \backslash$

$\backslash$hline $4\mathrm{.}7$ & $47$ & $470$ & $4700$ & $0\mathrm{.}047$ & $0\mathrm{.}47$ & $4\mathrm{.}7$ & $47$ & $470$ & $4700\backslash \backslash$

$\backslash$hline $5\mathrm{.}1$ & $51$ & $510$ & $5100$ & & & & & & $\backslash \backslash$

$\backslash$hline $5\mathrm{.}6$ & $56$ & $560$ & $5600$ & & & & & & $\backslash \backslash$

$\backslash$hline $6\mathrm{.}2$ & $62$ & $620$ & $6200$ & & & & & & $\backslash \backslash$

$\backslash$hline $6\mathrm{.}8$ & $68$ & $680$ & $6800$ & $0\mathrm{.}068$ & $0\mathrm{.}68$ & $6\mathrm{.}8$ & $68$ & $680$ & $6800\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$\backslash$begin$\{$tabular$\}\{|$r$|$r$|$r$|$r$|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$7\mathrm{.}5$ & $75$ & $750$ & $7500$ & & & & & & $\backslash \backslash$

$\backslash$hline $8\mathrm{.}2$ & $82$ & $820$ & $8200$ & & & & & & $\backslash \backslash$

$\backslash$hline $9\mathrm{.}1$ & $91$ & $910$ & $9100$ & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$