Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Next revision		 Previous revision
electrical_engineering_and_electronics_2:block08 [2026/04/21 03:58] – created mexleadminelectrical_engineering_and_electronics_2:block08 [2026/04/21 23:54] (current) – mexleadmin
Line 25: Line 25:
  
 ===== Conceptual overview ===== ===== Conceptual overview =====
-<callout icon="fa fa-lightbulb-o" color="blue"> +
-  - ... +
-</callout>+
  
 ===== Core content ===== ===== Core content =====
  
- +===== From Two-Terminal Network to Four-Terminal Network =====
- +
-====== 7 Networks at variable frequency ====== +
- +
-Further content can be found at this __ BROKEN-LINK:[[https://www.electronics-tutorials.ws/accircuits/series-circuit.html|Tutorial]] LINK-BROKEN __ or that [[https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-natural-and-forced-response/a/ee-rlc-natural-response-intuition|Tutorial]] +
- +
-==== Introduction ==== +
- +
-In the previous chapters, it was explained what the "influence of a sinusoidal current flow" of capacitors and inductors looks like. To describe this, the impedance was introduced. This can be understood as a complex resistance for sinusoidal excitation. +
- +
-It applies to the capacitor: +
- +
-\begin{align*}  +
-\underline{U}_C = \frac{1}{{\rm j}\omega \cdot C} \cdot \underline{I}_C \quad \rightarrow \quad  +
-\underline{Z}_C = \frac{1}{{\rm j}\omega \cdot C}  +
-\end{align*} +
- +
-and for the inductance +
- +
-\begin{align*}  +
-\underline{U}_L = {\rm j}\omega \cdot L \cdot \underline{I}_L \quad \rightarrow \quad  +
-\underline{Z}_L = {\rm j}\omega \cdot L  +
-\end{align*} +
- +
-Complex impedances can be dealt with in much the same way as ohmic resistances in Electrical Engineering 1 (see: [[:electrical_engineering_1:simple_circuits|simple DC Circuits]], [[electrical_engineering_1:non-ideal_sources_and_two_terminal_networks|linear Sources and two-terminal network]], [[:electrical_engineering_1:network_analysis|Analysis of DC Networks]]). In these transformations, the fraction $ j\omega \cdot$ is preserved. Circuits with impedances such as inductors and capacitors will show a frequency dependence accordingly. +
- +
-<callout> +
- +
-=== Targets === +
- +
-After this lesson, you should: +
- +
-  - know that … +
-  - know that … is formed. +
-  - be able to … can … +
- +
-</callout> +
- +
-===== 7.1 From Two-Terminal Network to Four-Terminal Network =====+
  
 <WRAP> <imgcaption imageNo01 | Two-Terminal Network to Four-Terminal Network> </imgcaption> \\ {{drawio>ZweipolundVierpol.svg}} \\ </WRAP> <WRAP> <imgcaption imageNo01 | Two-Terminal Network to Four-Terminal Network> </imgcaption> \\ {{drawio>ZweipolundVierpol.svg}} \\ </WRAP>
Line 102: Line 62:
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 7.2 RL Series Circuit =====+===== RL Series Circuit =====
  
 <WRAP> <imgcaption imageNo02 | RL-series> </imgcaption> \\ {{drawio>RLReihenschaltung.svg}} \\ <WRAP> <WRAP> <imgcaption imageNo02 | RL-series> </imgcaption> \\ {{drawio>RLReihenschaltung.svg}} \\ <WRAP>
Line 126: Line 86:
 These three points are now to be gone through. These three points are now to be gone through.
  
-==== 7.2.1 RL High Pass ====+==== RL High Pass ====
  
 For the first step, we investigate the limit consideration: We look at what happens when the frequency $\omega$ runs to the definition range limits, i.e. $\omega \rightarrow 0$ and $\omega \rightarrow \infty$: For the first step, we investigate the limit consideration: We look at what happens when the frequency $\omega$ runs to the definition range limits, i.e. $\omega \rightarrow 0$ and $\omega \rightarrow \infty$:
Line 154: Line 114:
 By this, the course from low to high frequencies is easier to see. The following simulation in <imgref imageNo5> shows the amplitude response and frequency response in the lower left corner. By this, the course from low to high frequencies is easier to see. The following simulation in <imgref imageNo5> shows the amplitude response and frequency response in the lower left corner.
  
-<WRAP centeralign>  
-<imgcaption imageNo5 | RL high pass filter>  
-</imgcaption>\\ 
-{{url>https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+4+1630997.1347384118%0Ar+64+80+224+80+0+35%0AO+224+80+336+80+0%0Ag+224+208+224+240+0%0A170+64+80+32+80+3+20+1000+5+0.1%0Al+224+80+224+208+0+0.001+0%0Ao+3+16+0+34+5+0.00009765625+0+-1+in%0Ao+1+16+0+34+2.5+0.00009765625+1+-1+out%0A 500,500 noborder}} 
-</WRAP> 
  
 +<imgcaption imageNo5|>[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+Infinity+0.75+50+5+50%0A%25+2+1183.069613694428%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0Ar+240+160+400+160+0+187%0Al+400+160+400+288+0+0.06545+0%0A170+240+160+208+160+3+20+1000+5+0.1%0A|{{:electrical_engineering_and_electronics_2:imageno5.jpg|click to start simulation}}]]  
 +</imgcaption>
  
 For further consideration, the equation of the transfer function $\underline{A} = \dfrac {\underline{U}_{\rm O}^\phantom{O}}{\underline{U}_{\rm I}^\phantom{O}}$ is to be rewritten so that it becomes independent of component values $R$ and $L$.\\  For further consideration, the equation of the transfer function $\underline{A} = \dfrac {\underline{U}_{\rm O}^\phantom{O}}{\underline{U}_{\rm I}^\phantom{O}}$ is to be rewritten so that it becomes independent of component values $R$ and $L$.\\ 
Line 236: Line 193:
 2 \pi f_{\rm c} &= \frac{R}{L} \quad \rightarrow \quad \boxed{f_{\rm c} = \frac{R}{2 \pi \cdot L}} \end{align*} 2 \pi f_{\rm c} &= \frac{R}{L} \quad \rightarrow \quad \boxed{f_{\rm c} = \frac{R}{2 \pi \cdot L}} \end{align*}
  
-==== 7.2.2 RL Low Pass ====+==== RL Low Pass ====
  
 <WRAP> <imgcaption imageNo04 | Circuit, pointer diagram, and amplitude and phase response of RL low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRLTiefpass.svg}} </WRAP> <WRAP> <imgcaption imageNo04 | Circuit, pointer diagram, and amplitude and phase response of RL low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRLTiefpass.svg}} </WRAP>
Line 251: Line 208:
 The cut-off frequency is again given by $f_{\rm c} = \frac{R}{2 \pi \cdot L}$. The cut-off frequency is again given by $f_{\rm c} = \frac{R}{2 \pi \cdot L}$.
  
-<WRAP centeralign>  +<imgcaption imageNo6|>[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+0.75+50+5+50%0A%25+2+24389.095776063856%0Ar+400+160+400+288+0+35%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0Al+240+160+400+160+0+0.06545+0%0A170+240+160+208+160+3+20+1000+5+0.1%0A|{{:electrical_engineering_and_electronics_2:imageno6.jpg|click to start simulation}}]]   
-<imgcaption imageNo6 | RL low pass filter>  +</imgcaption>
-</imgcaption>\\ +
-{{url>https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+4+1630997.1347384118%0Ar+224+208+224+80+0+35%0AO+224+80+336+80+0%0Ag+224+208+224+240+0%0A170+64+80+32+80+3+20+1000+5+0.1%0Al+64+80+224+80+0+0.001+0%0Ao+3+16+0+34+5+0.00009765625+0+-1+in%0Ao+1+16+0+34+2.5+0.00009765625+1+-1+out%0A 500,500 noborder}} +
-</WRAP>+
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 7.3 RC Series Circuit =====+===== RC Series Circuit =====
  
-==== 7.3.1 RC High Pass ====+==== RC High Pass ====
  
 <WRAP> <imgcaption imageNo05 | Circuit, pointer diagram, and amplitude and phase response of the RC high-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCHochpass.svg}} </WRAP> <WRAP> <imgcaption imageNo05 | Circuit, pointer diagram, and amplitude and phase response of the RC high-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCHochpass.svg}} </WRAP>
Line 282: Line 236:
 \end{align*} \end{align*}
  
-<WRAP centeralign>  +<imgcaption imageNo7|>[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+0.75+50+5+50%0A%25+0+28853.998118144256%0Ac+240+160+400+160+0+0.00001+0%0Ar+400+160+400+288+0+35%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0A170+240+160+208+160+3+20+1000+5+0.1%0A|{{:electrical_engineering_and_electronics_2:imageno7.jpg|click to start simulation}}]]   
-<imgcaption imageNo7 | RC high pass filter>  +</imgcaption> 
-</imgcaption>\\ +
-{{url>https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+4+1630997.1347384118%0Ac+64+80+224+80+0+0.000001+0%0Ar+224+80+224+208+0+35%0AO+224+80+336+80+0%0Ag+224+208+224+240+0%0A170+64+80+32+80+3+20+1000+5+0.1%0Ao+4+16+0+34+5+0.00009765625+0+-1+in%0Ao+2+16+0+34+2.5+0.00009765625+1+-1+out%0A 500,500 noborder}} +
-</WRAP>+
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== 7.3.2 RC Low Pass ====+==== RC Low Pass ====
  
 <WRAP> <imgcaption imageNo06 | Circuit, pointer diagram, and amplitude and phase response of RC low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCTiefpass.svg}} </WRAP> <WRAP> <imgcaption imageNo06 | Circuit, pointer diagram, and amplitude and phase response of RC low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCTiefpass.svg}} </WRAP>
Line 306: Line 258:
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-<WRAP centeralign>  +<imgcaption imageNo8|>[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+0.75+50+5+50%0A%25+0+28853.998118144256%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0Ar+240+160+400+160+0+187%0Ac+400+160+400+288+0+0.00001+0%0A170+240+160+208+160+3+20+1000+5+0.1%0A|{{:electrical_engineering_and_electronics_2:imageno8.jpg|click to start simulation}}]]   
-<imgcaption imageNo8 | RC low pass filter>  +</imgcaption>
-</imgcaption>\\ +
-{{url>https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+4+1630997.1347384118%0Ac+224+208+224+80+0+0.000001+0%0Ar+64+80+224+80+0+35%0AO+224+80+336+80+0%0Ag+224+208+224+240+0%0A170+64+80+32+80+3+20+1000+5+0.1%0Ao+4+16+0+34+5+0.00009765625+0+-1+in%0Ao+2+16+0+34+2.5+0.00009765625+1+-1+out%0A 500,500 noborder}} +
-</WRAP>+
  
 ==== RLC - Series Resonant Circuit ==== ==== RLC - Series Resonant Circuit ====
Line 394: Line 343:
 <accordion>  <accordion> 
 <panel title="Series Resonant Circuit in Time Domain (Voltage on Inductor)">  <panel title="Series Resonant Circuit in Time Domain (Voltage on Inductor)"> 
-<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l5AWAnC1b0DYrQEw8gOyFgAcYArBpBkQlgpCOSAgMxMCmAtGGAFAAlcDhIgk9UeKjgWcJtMYxyfAE7DJWfBums+AYxBaxmktsWx4CAtgSUwGZCWrkkpGlhhx+AG0OnjfqJgBB7YXiBcMATIGDjRkE4EcZDkCFB8AOaB4CHZRop8+NYi2qzkOAFpAPYArgAufFXSEIwMSEHmLYbykHysoowAYhDsDIxg8BEQgyocAI41HAB2egCefEA 500,400 noborder}}  +<imgcaption imageNo51|> 
-</WRAP> </panel> +[[https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l5AWAnC1b0DYrQEw8gOyFgAcYArBpBkQlgpCOSAgMxMCmAtGGAFAAlcDhIgk9UeKjgWcJtMYxyfAE7DJWfBums+AYxBaxmktsWx4CAtgSUwGZCWrkkpGlhhx+AG0OnjfqJgBB7YXiBcMATIGDjRkE4EcZDkCFB8AOaB4CHZRop8+NYi2qzkOAFpAPYArgAufFXSEIwMSEHmLYbykHysoowAYhDsDIxg8BEQgyocAI41HAB2egCefEA|{{electrical_engineering_and_electronics_2:imageno51.jpg|click to start simulation}}]]   
 +</imgcaption> 
 +</panel> 
  
 <panel title="Series Resonant Circuit in Frequency Domain (Voltage on Inductor)">  <panel title="Series Resonant Circuit in Frequency Domain (Voltage on Inductor)"> 
-<WRAP>{{url>https://falstad.com/afilter/circuitjs.html?running=false&cct=$+1+0.000005+5+50+5+50%0A%25+4+1959.030510288011%0Ac+256+80+304+80+0+0.000047+0%0Ar+192+80+256+80+0+3%0Ag+304+160+304+192+0%0A170+192+80+160+80+3+20+1000+5+0.1%0Al+304+160+304+80+0+0.01+0.46265716582988115%0AO+304+80+352+80+0%0Ao+3+16+0+34+5+0.00009765625+0+-1+in%0A 500,400 noborder}}  +<imgcaption imageNo52|> 
-</WRAP> </panel> +[[www.falstad.com/afilter/circuitjs.html?cct=$+1+Infinity+0.75+50+5+50%0A%25+0+303633.8585081898%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0Ar+176+160+288+160+0+3%0Ac+400+160+288+160+0+0.000047+0%0A170+176+160+144+160+3+20+1000+5+0.1%0Al+400+288+400+160+0+0.001+0%0A|{{electrical_engineering_and_electronics_2:imageno52.jpg|click to start simulation}}]] 
 +</imgcaption> 
 +</panel> 
  
 <panel title="Series Resonant Circuit in Frequency Domain (Voltage on Capacitor)">  <panel title="Series Resonant Circuit in Frequency Domain (Voltage on Capacitor)"> 
-<WRAP>{{url>https://falstad.com/afilter/circuitjs.html?running=false&cct=$+1+0.000005+5+50+5+50%0A%25+4+1959.030510288011%0Ac+304+160+304+80+0+0.000047+0%0Ar+192+80+256+80+0+3%0Ag+304+160+304+192+0%0A170+192+80+160+80+3+20+1000+5+0.1%0Al+256+80+304+80+0+0.01+0.46265716582988115%0AO+304+80+352+80+0%0Ao+3+16+0+34+5+0.00009765625+0+-1+in%0A 500,400 noborder}}  +<imgcaption imageNo53|> 
-</WRAP> ~~PAGEBREAK~~ ~~CLEARFIX~~ </panel> +[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+Infinity+0.75+50+5+50%0A%25+0+303633.8585081898%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0Ar+176+160+288+160+0+3%0Ac+400+160+400+288+0+0.000047+0%0A170+176+160+144+160+3+20+1000+5+0.1%0Al+288+160+400+160+0+0.001+0%0A|{{electrical_engineering_and_electronics_2:imageno53.jpg|click to start simulation}}]] 
 +</imgcaption> 
 +</panel> 
  
 <panel title="Series Resonant Circuit in Frequency Domain (Voltage on Resistor)">  <panel title="Series Resonant Circuit in Frequency Domain (Voltage on Resistor)"> 
-<WRAP>{{url>https://falstad.com/afilter/circuitjs.html?running=false&cct=$+1+0.000005+5+50+5+50%0A%25+4+1959.030510288011%0Ac+192+80+256+80+0+0.000047+0%0Ar+304+80+304+160+0+3%0Ag+304+160+304+192+0%0A170+192+80+160+80+3+20+1000+5+0.1%0Al+256+80+304+80+0+0.01+0.46265716582988115%0AO+304+80+352+80+0%0Ao+3+16+0+34+5+0.00009765625+0+-1+in%0A 500,400 noborder}}  +<imgcaption imageNo54|> 
-</WRAP> </panel> +[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+Infinity+0.75+50+5+50%0A%25+0+303633.8585081898%0AO+400+160+512+160+0%0Ag+400+288+400+320+0%0Ar+400+160+400+288+0+3%0Ac+176+160+288+160+0+0.000047+0%0A170+176+160+144+160+3+20+1000+5+0.1%0Al+288+160+400+160+0+0.001+0%0A|{{electrical_engineering_and_electronics_2:imageno54.jpg|click to start simulation}}]] 
 +</imgcaption> 
 +</panel> 
  
 <panel title="Parallel Resonant Circuit in Frequency Domain (Voltage on Resistor)">  <panel title="Parallel Resonant Circuit in Frequency Domain (Voltage on Resistor)"> 
-<WRAP>{{url>https://falstad.com/afilter/circuitjs.html?running=false&cct=$+1+0.000005+5+50+5+50%0A%25+4+17425.09278334521%0Ac+176+96+176+16+0+0.00038999999999999994+0%0Ag+240+144+240+176+0%0A170+128+16+96+16+3+20+1000+5+0.1%0Al+240+96+240+16+0+0.00009999999999999999+7.7025416617456886%0AO+240+96+288+96+0%0Aw+128+16+176+16+0%0Ar+240+96+240+144+0+0.1%0Aw+176+96+240+96+0%0Aw+240+16+176+16+0%0Ao+2+16+0+34+5+0.00009765625+0+-1+in%0A 500,400 noborder}}  +<imgcaption imageNo55|> 
-</WRAP> </panel> </accordion>+[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+Infinity+0.75+50+5+50%0A%25+0+303633.8585081898%0AO+368+288+416+288+0%0Ag+336+368+336+400+0%0Ar+336+288+336+368+0+1%0Ac+304+288+304+160+0+0.000047+0%0A170+304+160+256+160+3+20+1000+5+0.1%0Al+368+288+368+160+0+0.001+0%0Aw+304+160+368+160+0%0Aw+304+288+336+288+0%0Aw+368+288+336+288+0%0A|{{electrical_engineering_and_electronics_2:imageno55.jpg|click to start simulation}}]] 
 +</imgcaption> 
 +</panel>  
 +</accordion>
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 6.4 Applications of Inductors =====+===== Applications of Inductors =====
  
   * ferrite bead   * ferrite bead
Line 422: Line 382:
   * unwanted coupling and circuit design   * unwanted coupling and circuit design
  
-===== 6.5 Examples =====+===== Examples =====
  
 === Decoupling Capacitor on the Microcontroller === === Decoupling Capacitor on the Microcontroller ===
Line 434: Line 394:
 [[https://www.electronics-tutorials.ws/oscillator/crystal.html|more background]] [[https://www.electronics-tutorials.ws/oscillator/crystal.html|more background]]
  
-Simulation in Time Domain <WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCBMCmC0CcIAMA6SA2JB2AzAFi0izByXgyyyhyhQFYQ8a64wwAoAcxCwA49GYdD36MckZMnYBjEQPFI5IHOl6ScrCIqTsA7krCQ1veMMNqdssEl5qF4G3dXrNknfpNmjIeOXDf3Hzx5SEVfCXtAz2VQoJDtGR8-cySI2MU8VwSAGxBo0ONTfwtkFCRytl8q6prEVCQtMo5ZfLphfJtJPBQ8cr7+-rBWCQSAJzyi+1bhbRQObmtbQTNHMRGpcb4BPCElFRKh2EN2AA8HJAkChzBESDZGKAEAYVOfMAY74XhxKBuHyGer2+lwBQUUkCID0MIAAyq9rH9Pg5IB8-gJoToAEZ5PBqNjopAqZREwKLOyxcIxBJnaI4OgE8rKOhUdHGACyAAkAF4AHQAztJRgBPPkAFwAhtkge8oFgBMDZSzHiAAEpAulQXgSeBMTUMdESOHvCDwaGwH7WTrm9brOjsAAybwksFxeXQAhdBxAADNJXzoCAGIFTc7dlsQEcZnolJG9iNo2SIxbymprRsHEsdislvtJIdjuNE2nEz9FJbygnVu6M+SEvpw9XwykdJtRMmc+ty311WX0NqcHj0Pr-LDpTR3vKMOBmf8BPb4e9wWZ3pdEAaQABLBekcB4sAEX6z1ULu7EiBsfDE7Yj+2QBdIELjwwQcTCASgl5nLDwck0Xgy18j0-PIAJwCAtTsS913tDh6zbWImwCdhsTlCBYD4cAhDXCxpTULAywfCBcChNQNwAOz5DcABNoH5UUAAtaL5NkngAVXYUIqAbAR-2EasBAAeRhJ5+QASQAOQ47AaxAas2FifiQCEkS+QE1iABVo24uMpH0RM5NWUspKoIsLUMRQ0wEAARDdOA3CVsn5NTNK-dAqBdBh+A9PAJHRQThP5ABRMjxUxbJoHYAB7MRwC6awJCDMo+ngLAhz7IMoBimhlLEyTouCWKMnihxSn6FK0pRSRfPkJSAtUjSosYEy4ouQNSuS1K2kq8EmuUEAbLshynIaoA 800,800 noborder}} </WRAP>+[[https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCBMCmC0CcIAMA6SA2JB2AzAFi0izByXgyyyhyhQFYQ8a64wwAoAcxCwA49GYdD36MckZMnYBjEQPFI5IHOl6ScrCIqTsA7krCQ1veMMNqdssEl5qF4G3dXrNknfpNmjIeOXDf3Hzx5SEVfCXtAz2VQoJDtGR8-cySI2MU8VwSAGxBo0ONTfwtkFCRytl8q6prEVCQtMo5ZfLphfJtJPBQ8cr7+-rBWCQSAJzyi+1bhbRQObmtbQTNHMRGpcb4BPCElFRKh2EN2AA8HJAkChzBESDZGKAEAYVOfMAY74XhxKBuHyGer2+lwBQUUkCID0MIAAyq9rH9Pg5IB8-gJoToAEZ5PBqNjopAqZREwKLOyxcIxBJnaI4OgE8rKOhUdHGACyAAkAF4AHQAztJRgBPPkAFwAhtkge8oFgBMDZSzHiAAEpAulQXgSeBMTUMdESOHvCDwaGwH7WTrm9brOjsAAybwksFxeXQAhdBxAADNJXzoCAGIFTc7dlsQEcZnolJG9iNo2SIxbymprRsHEsdislvtJIdjuNE2nEz9FJbygnVu6M+SEvpw9XwykdJtRMmc+ty311WX0NqcHj0Pr-LDpTR3vKMOBmf8BPb4e9wWZ3pdEAaQABLBekcB4sAEX6z1ULu7EiBsfDE7Yj+2QBdIELjwwQcTCASgl5nLDwck0Xgy18j0-PIAJwCAtTsS913tDh6zbWImwCdhsTlCBYD4cAhDXCxpTULAywfCBcChNQNwAOz5DcABNoH5UUAAtaL5NkngAVXYUIqAbAR-2EasBAAeRhJ5+QASQAOQ47AaxAas2FifiQCEkS+QE1iABVo24uMpH0RM5NWUspKoIsLUMRQ0wEAARDdOA3CVsn5NTNK-dAqBdBh+A9PAJHRQThP5ABRMjxUxbJoHYAB7MRwC6awJCDMo+ngLAhz7IMoBimhlLEyTouCWKMnihxSn6FK0pRSRfPkJSAtUjSosYEy4ouQNSuS1K2kq8EmuUEAbLshynIaoA|Simulation in Time Domain]]
  
-Simulation in Frequency Domain <WRAP>{{url>https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+4+252791342.77679944%0A170+448+48+416+48+3+20+1000+5+0.1%0Ax+695+186+703+189+4+12+S%0Ax+675+178+692+181+4+24+R%0Ax+820+37+924+40+4+18+8MHz+crystal%0Ax+378+102+544+105+4+18+linear+voltage+source%0Aw+512+48+576+48+0%0Ax+803+130+809+133+4+12+0%0Ax+695+131+703+134+4+12+S%0Ax+678+123+695+126+4+24+C%0Ax+786+122+803+125+4+24+C%0AO+848+144+912+144+0%0Ar+448+48+512+48+0+1%0Ar+656+208+656+160+0+0.1%0Ac+656+160+656+112+0+4.400000000000001e-12+-5.033145800262313%0Al+656+112+656+48+0+0.00009499999999999999+0%0Ac+752+48+752+208+0+5e-11+-0.6291750159603016%0Aw+656+208+752+208+0%0Aw+656+48+752+48+0%0Aw+576+48+656+48+0%0Ac+576+112+576+48+0+3e-11+0.0012090544090004919%0Ag+576+112+576+144+0%0Aw+752+208+800+208+2%0AB+384+16+528+80+2+Box%0Ag+848+208+848+224+0%0Ac+848+208+848+144+0+3e-11+0.0012090544090004919%0AB+624+16+816+240+2+Box%0Aw+800+208+800+144+0%0Aw+800+144+848+144+0%0Ao+0+16+0+34+5+0.00009765625+0+-1+in%0A noborder}} </WRAP>+[[https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+0.75+50+5+50%0A%25+4+252791342.77679944%0A170+448+48+416+48+3+20+1000+5+0.1%0Ax+695+186+703+189+4+12+S%0Ax+675+178+692+181+4+24+R%0Ax+820+37+924+40+4+18+8MHz+crystal%0Ax+378+102+544+105+4+18+linear+voltage+source%0Aw+512+48+576+48+0%0Ax+803+130+809+133+4+12+0%0Ax+695+131+703+134+4+12+S%0Ax+678+123+695+126+4+24+C%0Ax+786+122+803+125+4+24+C%0AO+848+144+912+144+0%0Ar+448+48+512+48+0+1%0Ar+656+208+656+160+0+0.1%0Ac+656+160+656+112+0+4.400000000000001e-12+-5.033145800262313%0Al+656+112+656+48+0+0.00009499999999999999+0%0Ac+752+48+752+208+0+5e-11+-0.6291750159603016%0Aw+656+208+752+208+0%0Aw+656+48+752+48+0%0Aw+576+48+656+48+0%0Ac+576+112+576+48+0+3e-11+0.0012090544090004919%0Ag+576+112+576+144+0%0Aw+752+208+800+208+2%0AB+384+16+528+80+2+Box%0Ag+848+208+848+224+0%0Ac+848+208+848+144+0+3e-11+0.0012090544090004919%0AB+624+16+816+240+2+Box%0Aw+800+208+800+144+0%0Aw+800+144+848+144+0%0A|Simulation in Frequency Domain]]
  
 [[https://www.falstad.com/circuit/crystal.html|setup for the design]] [[https://www.falstad.com/circuit/crystal.html|setup for the design]]