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electrical_engineering_and_electronics_2:block11 [2026/06/02 00:50] – mexleadminelectrical_engineering_and_electronics_2:block11 [2026/06/10 03:08] (current) – mexleadmin
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 \] \]
 at a qualitative level. at a qualitative level.
-  * calculate simple diode operating points with a series resistor. 
-  * identify basic diode types such as universal diodes, Z-diodes, and LEDs. 
 </callout> </callout>
  
Line 78: Line 76:
  
 ===== Core content ===== ===== Core content =====
- 
-<callout> A nice introduction to the bipolar transistor can be found in [[http://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Materials_and_Devices/Bipolar_Junction_Transistor|libretexts]]. Some of the following passages, videos and pictures are taken from this introduction. </callout> 
  
 <WRAP><callout type="info" icon="true"> <WRAP><callout type="info" icon="true">
Line 112: Line 108:
 <WRAP> <WRAP>
 <panel type="default"> <panel type="default">
-<imgcaption sep_Res|sepcific resistance for selected conductors, semiconductors, and insulators.></imgcaption>+<imgcaption sep_Res|specific resistance for selected conductors, semiconductors, and insulators.></imgcaption>
 {{drawio>block11_specResistanceV02.svg}} {{drawio>block11_specResistanceV02.svg}}
 </panel> </panel>
Line 407: Line 403:
 ^ Symbol ^ Meaning ^ ^ Symbol ^ Meaning ^
 | \(I_{\rm S}(T)\) | reverse saturation current, strongly temperature-dependent  | | \(I_{\rm S}(T)\) | reverse saturation current, strongly temperature-dependent  |
-| \(m\) | emission coefficient, typically \(1\ldots 2\)  |+| \(m\) | emission coefficient, typically \(1\ldots 2\), material constant  |
 | \(U_{\rm T}\) | thermal voltage ($U_{\rm T}\approx 26~{\rm mV}$ at room temperature)  | | \(U_{\rm T}\) | thermal voltage ($U_{\rm T}\approx 26~{\rm mV}$ at room temperature)  |
 | \(k\) | Boltzmann constant  | | \(k\) | Boltzmann constant  |
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 {{url>https://www.falstad.com/circuit/circuitjs.html?hideSidebar=true&ctz=CQAgjA7CAMB00OgVhrAbAJiQFgggnEmPgMxokkgAcKGIS09ApgLRhgBQARuPnWNmz0MQso2gcAHiAwkw4OSGxh+JIUIyMATkwCGAGwA6AZwAmASwD2ppiYAUARobQAtgDUAlBwDmMkTKoqP1FNGBgONXAAOWVsKgB9MOxYEiQMVnxUNGwkILBYfGg0cDBxDlNgmWggjH8MQJlo2ISOACVKzRr-SGLGSgZUFHFBjmxoSgwIfghiojpUukZseOz46HjlNAh4-KxWJDR4qn3tsHiMDfiSNpA2eqqgu7yZsP7xAqGwuCRy25Ua6p-e71GpNAQtXxPAKPf4gCi9cLSFj4eQqTKFBR0DTaPRGMxWGz2ByEVyebh-NCMARCSDzSnhMaUFhUKkvMD0hZhbZzNYbdlnJAZQ75NBC3kXbbXaTYYpgGj0VENGlBACSUjh+DyVHkjPAVHUepAaukYDSARQ7I0SsNAFV1Qx5PV+mAJlRisqQHbpBArbL2AFMh64BA3OrSo60JlSrQpkpDQAfdWCK2B7UyPhxuWobCh6VbGQQHWFgsGrOJ6QYfCZERQOSOgYer1w00yHBwrCtqAegBaNyhcUY-bir3o70ow2+v37LKBQQOjH4MXB8R8s-o9KhSAzZV1zKWw-ZjEwQgXJHiPPWmwFrDiGxvh3WF1kV3JbHISnZ4EjIHIi3Vd3UcZ6C7Io41CHQDBMCxrFsYxHBIBB3C8aVKByVCghyd1DWNcAZXoJALVyfCMNtdU8HXGloCgA4u0NOAMFzEAUXoQQmJQHBaLLf8DgVTIWFYtIsVIpExmEYoWAQ4RA0NXtpBISs-EoEg01qLCs1KaBAB7gABBdVlKgDABA1AzIEzIIVyRTJnBkN5UMNMAdL0lBsFIJRnPwNTzL0iZiCUCZajMkALNuOoFIoGyhPUxDdKRdggnwdQfSY2j-GgwljAAYwAC10LRdAygAXJgtHMYwCvMDKoKYAAHJgADsLDq7wTEsOqTAAN0sfQCt0bwmAAegygBXLQdDqgqTDypqmHVWoMKAkh8BArDwNxKCCVgxwGCQ1daiEedKi3RZwgqPalBnM6DsXZoV3aM6B0qQQgj6UdUGQL4Rl1SYsWHOYf38JYz1KEReU2M80FgEQq2hmGYdYSB4nwWAZgOPYWEM8UNjPa4eGILEjLSIRyDKOTNTcnUgJyUtVXtaB5AI51+h4xskw7VHzroA5nLo+AsEY7BUhY5zFpYkiuIrKsFVrf00iWYTm3Y-x5MVziglkhWlAzZSsUIQK4AQJBHLkt1NaUjzNc8oKOCAA noborder}}  {{url>https://www.falstad.com/circuit/circuitjs.html?hideSidebar=true&ctz=CQAgjA7CAMB00OgVhrAbAJiQFgggnEmPgMxokkgAcKGIS09ApgLRhgBQARuPnWNmz0MQso2gcAHiAwkw4OSGxh+JIUIyMATkwCGAGwA6AZwAmASwD2ppiYAUARobQAtgDUAlBwDmMkTKoqP1FNGBgONXAAOWVsKgB9MOxYEiQMVnxUNGwkILBYfGg0cDBxDlNgmWggjH8MQJlo2ISOACVKzRr-SGLGSgZUFHFBjmxoSgwIfghiojpUukZseOz46HjlNAh4-KxWJDR4qn3tsHiMDfiSNpA2eqqgu7yZsP7xAqGwuCRy25Ua6p-e71GpNAQtXxPAKPf4gCi9cLSFj4eQqTKFBR0DTaPRGMxWGz2ByEVyebh-NCMARCSDzSnhMaUFhUKkvMD0hZhbZzNYbdlnJAZQ75NBC3kXbbXaTYYpgGj0VENGlBACSUjh+DyVHkjPAVHUepAaukYDSARQ7I0SsNAFV1Qx5PV+mAJlRisqQHbpBArbL2AFMh64BA3OrSo60JlSrQpkpDQAfdWCK2B7UyPhxuWobCh6VbGQQHWFgsGrOJ6QYfCZERQOSOgYer1w00yHBwrCtqAegBaNyhcUY-bir3o70ow2+v37LKBQQOjH4MXB8R8s-o9KhSAzZV1zKWw-ZjEwQgXJHiPPWmwFrDiGxvh3WF1kV3JbHISnZ4EjIHIi3Vd3UcZ6C7Io41CHQDBMCxrFsYxHBIBB3C8aVKByVCghyd1DWNcAZXoJALVyfCMNtdU8HXGloCgA4u0NOAMFzEAUXoQQmJQHBaLLf8DgVTIWFYtIsVIpExmEYoWAQ4RA0NXtpBISs-EoEg01qLCs1KaBAB7gABBdVlKgDABA1AzIEzIIVyRTJnBkN5UMNMAdL0lBsFIJRnPwNTzL0iZiCUCZajMkALNuOoFIoGyhPUxDdKRdggnwdQfSY2j-GgwljAAYwAC10LRdAygAXJgtHMYwCvMDKoKYAAHJgADsLDq7wTEsOqTAAN0sfQCt0bwmAAegygBXLQdDqgqTDypqmHVWoMKAkh8BArDwNxKCCVgxwGCQ1daiEedKi3RZwgqPalBnM6DsXZoV3aM6B0qQQgj6UdUGQL4Rl1SYsWHOYf38JYz1KEReU2M80FgEQq2hmGYdYSB4nwWAZgOPYWEM8UNjPa4eGILEjLSIRyDKOTNTcnUgJyUtVXtaB5AI51+h4xskw7VHzroA5nLo+AsEY7BUhY5zFpYkiuIrKsFVrf00iWYTm3Y-x5MVziglkhWlAzZSsUIQK4AQJBHLkt1NaUjzNc8oKOCAA noborder}} 
 </WRAP> </WRAP>
 +
 +==== Practical diode models for circuit calculation ====
 +
 +For hand calculations we usually do not use the full exponential equation, because it is often too complex for a quick solution. \\
 +Instead the following is often used:
 +
 +<tabcaption tab_diode_models|Diode models for circuit calculations>
 +
 +^ Model ^ Forward direction ^ Reverse direction ^ Use ^ Example ^
 +| ideal diode             | \(u_{\rm AK}=0\)                                     |  \(i_{\rm D}=0\)         | switching logic, first estimate   | Is the rectifier path conducting?      |
 +| constant-voltage model  | \(u_{\rm AK}\approx U_{\rm TO}\)                     |  \(i_{\rm D}\approx 0\)  | quick current calculations        | Which current flows through an LED and its series resistor?  |
 +| piecewise-linear model  | \(u_{\rm AK}\approx U_{\rm TO}+r_{\rm F}\cdot i_{\rm D}\)  |  \(i_{\rm D}\approx 0\)  | more accurate operating point     | How does the diode voltage change when the current changes?  |
 +</tabcaption>
 +\\ 
 +<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=DwYwlgTgBAZgvAIgIwHYFQC4GdEAYB0uRuArOmCIkvgCwDMAnEkwGy4MlI0MAcDd6EACNEJXOgAOIhGPQA3CFXQBbbKICmAWiRIEAPgBQUKMCFQAHohYkWUJACYeUDrbpt08BOID0h48HMLKx4nHVwoFH47JAFYRBp0LDBEewTMdUQIdQBDABsoABMwAHsC9QRfIxMAcyCEFhCoOntwhqc6Nw88Cr8TArq2uwZ7KEHm8TiEexViqgA5GiIEyv8AJQHG5hHBpHdJiYB3T1iYRRkJ5WzzOTx8Hh6q4ABlEGKJdTqUXBo7NmcaH4dFhdLz6Kr+YpQdQAO3iiQkVjSnnM9EkiG0YOMWJMEigN1BUCwlGQhC4Dm+PFwSB49hIPE6K2xOLxiFiRNuu3stOGKAa9mGMToaEZ-m8xV6wG8Lze6glgUsCGGTnsKBGDEWUBVZEmaSSVHu6UQAFUHv55Yh6eFdk56SQ7ChdDrEslkAaMBkEABJU0mc0IHgoFCa1XOLjB7WeXUu6nod23FAANR9wDkdSQRGVIfTuGVqRBh08Fyu+IIwol0AV2dCwzsGc1ef26DOukZATTdbC0Qa0ROcMJLobcYQYDKeTAAC91P0iqVyq3apW6+Nazmmp1G62CsooNDlIgYAcChA3nACFT8+QcMgtGgoBArxNYV5CA2hCXk-1F6uVSMq00WiC0xQMoswIAeR4nmeLYSusX7Vr+HZ7IW6BHKyHhnLIwHFrc9yttK7zthquxWo44RAhevQQlCT5cPCVC4A2yI0EBCIIBilFYsAuLvoSxIEAw6osDQQmqjwzAkCgHQ+tiXEsggbJ8fgSAkEw9D0DYnAxKgAgiiYYoSlKrzvBKZgKrwv6OHY-LtEh3Stn6DgsLY9jdg4KCZo6kbOvqsYeia9lprsthBdEDq-AwIJRj5hpesmDn2GGKokZwwa9ggUWur58ZJpUkrgBAhhAA noborder}} \\ </WRAP>
 +
 +
 +The differential forward resistance is
 +
 +\[
 +\begin{align*}
 +r_{\rm F}
 +=
 +\frac{\Delta U_{\rm F}}{\Delta I_{\rm F}}.
 +\end{align*}
 +\]
 +
 +For large forward voltages compared with \(U_{\rm T}\), the diode equation leads approximately to
 +
 +\[
 +\begin{align*}
 +r_{\rm D}
 +=
 +\frac{{\rm d}u_{\rm D}}{{\rm d}i_{\rm D}}
 +\approx
 +\frac{mU_{\rm T}}{I_{\rm D}}.
 +\end{align*}
 +\]
 +
 +<callout type="info" icon="true">
 +**Unit check**
 +
 +\[
 +\begin{align*}
 +[r_{\rm D}]
 +=
 +\frac{[U_{\rm T}]}{[I_{\rm D}]}
 +=
 +\frac{{\rm V}}{{\rm A}}
 +=
 +\Omega.
 +\end{align*}
 +\]
 +</callout>
  
 ===== Exercises ===== ===== Exercises =====
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}=5.0~{\rm V},+U_{\rm I}=5.0~{\rm V},
 \qquad \qquad
 R=1.0~{\rm k}\Omega. R=1.0~{\rm k}\Omega.
Line 546: Line 596:
 U_R U_R
 = =
-U_{\rm E}-U_{\rm D}+U_{\rm I}-U_{\rm D}
 = =
 5.0~{\rm V}-0.7~{\rm V} 5.0~{\rm V}-0.7~{\rm V}
Line 631: Line 681:
 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}=12~{\rm V},+U_{\rm I}=12~{\rm V},
 \qquad \qquad
 R=560~\Omega. R=560~\Omega.
Line 669: Line 719:
 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}+U_{\rm I}
 = =
 RI_{\rm D} RI_{\rm D}
Line 681: Line 731:
 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}+U_{\rm I}
 = =
 RI_{\rm D} RI_{\rm D}
Line 697: Line 747:
 I_{\rm D} I_{\rm D}
 = =
-\frac{U_{\rm E}-U_{\rm TO}}{R+r_{\rm F}}.+\frac{U_{\rm I}-U_{\rm TO}}{R+r_{\rm F}}.
 \end{align*} \end{align*}
 \] \]
Line 781: Line 831:
  
 ===== Embedded resources ===== ===== Embedded resources =====
- 
-<WRAP group> 
-<WRAP column half> 
-<panel type="info" title="PhET: Semiconductors"> 
-Use this simulation to explore doping and the formation of a diode. 
- 
-{{url>https://phet.colorado.edu/en/simulations/semiconductor 700,500 noborder}} 
-</panel> 
-</WRAP> 
- 
-<WRAP column half> 
-<panel type="info" title="Falstad: Diode I/V curve"> 
-Use this simulation to compare a resistor characteristic with the nonlinear diode characteristic. 
- 
-{{url>https://www.falstad.com/circuit/e-diodecurve.html 700,500 noborder}} 
-</panel> 
-</WRAP> 
-</WRAP> 
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~