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electrical_engineering_and_electronics_2:block11 [2026/06/02 00:02] – mexleadminelectrical_engineering_and_electronics_2:block11 [2026/06/10 03:08] (current) – mexleadmin
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-TBD 
- 
-  - Semiconductor components \\ (approx. 4 blocks, based on previous lectures on [[circuit_design:2_diodes|Diodes]] and [[circuit_design:2_transistors|Transistors]] ) 
-    - Fundamentals (conductors, semiconductors, insulators, doping, band model, intrinsic conductivity) 
-    - Diodes (real characteristic curve, operating point, equivalent circuit) 
-    - Zener diode 
-    - LED 
-    - Protective circuit with diodes 
-    - Rectifier circuits (single-phase rectifier, center tap circuit, bridge rectifier, smoothing capacitor) 
-    - Bipolar transistor (structure, designations, characteristic curve, characteristic values) 
-    - Transistor as a switch (circuit, switching times and behavior) 
-    - MOSFET (structure, comparison with bipolar transistor) 
-    - Optional: Transistor as an amplifier 
- 
- 
 ====== Block 11 — Semiconductor Fundamentals and Diodes ====== ====== Block 11 — Semiconductor Fundamentals and Diodes ======
  
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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>
  
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 ===== 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">
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 <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>
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   * \(u_{\rm AK}>0\): anode is more positive than cathode.   * \(u_{\rm AK}>0\): anode is more positive than cathode.
-  * \(u_{\rm AK}<0\): anode is more negative than cathode. +  * \(u_{\rm AK}<0\): anode is more negative than cathode.  
 +\\ \\
 <tabcaption tab_diode_bias|Diode operation depending on \(u_{\rm AK}\)> <tabcaption tab_diode_bias|Diode operation depending on \(u_{\rm AK}\)>
  
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 | \(u_{\rm AK}<0\) | reverse bias \\ reverse voltage is $U_{\rm R} = -u_{\rm AK}$  | depletion region becomes larger | only small leakage current, until breakdown  | | \(u_{\rm AK}<0\) | reverse bias \\ reverse voltage is $U_{\rm R} = -u_{\rm AK}$  | depletion region becomes larger | only small leakage current, until breakdown  |
 </tabcaption> </tabcaption>
 +\\ 
  
 <WRAP> <WRAP>
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 \] \]
  
-<WRAP> +<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=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-xAQCNhwYgUEgX9v0gaYoIASVBTA4PEQRMDLcAIF-cBBAwjZMEIUC8wguFiJgAAaCAADVOCAA noborder}} </WRAP>
-<panel type="default"> +
-<imgcaption fig_ideal_diode_characteristic|Ideal diode characteristic.></imgcaption> +
-{{drawio>block11_ideal_diode_characteristic.svg}} +
-</panel> +
-</WRAP>+
  
 <panel type="info" title="Engineering meaning"> <panel type="info" title="Engineering meaning">
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 ^ 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 | +| \(U_{\rm T}\) | thermal voltage ($U_{\rm T}\approx 26~{\rm mV}$ at room temperature)  | 
-| \(k\) | Boltzmann constant | +| \(k\) | Boltzmann constant  | 
-| \(e\) | elementary charge | +| \(e\) | elementary charge  | 
-| \(T\) | absolute temperature in \({\rm K}\) |+| \(T\) | absolute temperature in \({\rm K}\)  | 
 +</tabcaption> 
 +\\
  
-At room temperature, \(U_{\rm T}\) is approximately +Often a **turn-on voltage** $U_{\rm TO}$ for typical currents (some $\rm mA$) at \(25^\circ{\rm C}\) are used.
- +
-\[ +
-\begin{align*} +
-U_{\rm T}\approx 26~{\rm mV}. +
-\end{align*} +
-\] +
- +
-Typical values at \(25^\circ{\rm C}\):+
  
 <tabcaption tab_typical_diode_values|Typical diode values> <tabcaption tab_typical_diode_values|Typical diode values>
  
-^ Diode material ^ Approximate threshold voltage \(U_{\rm TO}\) ^ Reverse saturation current \(I_{\rm S}\) ^+^  Diode material \\  ^  Approximate threshold \\ voltage \(U_{\rm TO}\)  ^  Reverse saturation \\ current \(I_{\rm S}\)  ^
 | silicon | \(\approx 0.7~{\rm V}\) | some \({\rm pA}\) | | silicon | \(\approx 0.7~{\rm V}\) | some \({\rm pA}\) |
 | germanium | \(\approx 0.3~{\rm V}\) | some \(\mu{\rm A}\) | | germanium | \(\approx 0.3~{\rm V}\) | some \(\mu{\rm A}\) |
 +</tabcaption>
 +
  
 <callout type="warning" icon="true"> <callout type="warning" icon="true">
-The value \(0.7~{\rm V}\) for a silicon diode is not a physical constant.   +  * the turn-on voltage has also some alternative labeling: knee voltage, threshold voltage, diode voltage $U_{\rm D}$, forward voltage $U_{\rm F}$ 
-It is a useful approximation for typical currents in small signal and basic power circuits.+  * The value \(U_{\rm TO} = 0.7~{\rm V}\) for a silicon diode is not a physical constant.  
 +  * It is a useful approximation for typical currents in small signal and basic power circuits.
 </callout> </callout>
 +
 +<WRAP>
 +{{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>
  
 ==== Practical diode models for circuit calculation ==== ==== Practical diode models for circuit calculation ====
  
-For hand calculations we usually do not use the full exponential equation.+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:
  
-<WRAP> +<tabcaption tab_diode_models|Diode models for circuit calculations>
-<panel type="default"> +
-<imgcaption fig_diode_models|Comparison of ideal, constant-voltage, and piecewise-linear diode models.></imgcaption> +
-{{drawio>block11_diode_models.svg}} +
-</panel> +
-</WRAP>+
  
-<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>
  
-^ Model ^ Forward direction ^ Reverse direction ^ Use ^ 
-| ideal diode | \(u_{\rm AK}=0\) | \(i_{\rm D}=0\) | switching logic, first estimate | 
-| constant-voltage model | \(u_{\rm AK}\approx U_{\rm TO}\) | \(i_{\rm D}\approx 0\) | quick current calculations | 
-| piecewise-linear model | \(u_{\rm AK}\approx U_{\rm TO}+r_{\rm F}i_{\rm D}\) | \(i_{\rm D}\approx 0\) | more accurate operating point | 
  
 The differential forward resistance is The differential forward resistance is
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 \] \]
 </callout> </callout>
- 
-==== Operating point with a series resistor ==== 
- 
-A diode must usually be operated with a current-limiting element. 
- 
-For the circuit 
- 
-\[ 
-\begin{align*} 
-U_{\rm E} 
-\rightarrow R 
-\rightarrow D 
-\end{align*} 
-\] 
- 
-the loop equation is 
- 
-\[ 
-\begin{align*} 
-U_{\rm E} 
-= 
-U_R+U_{\rm D}. 
-\end{align*} 
-\] 
- 
-With the constant-voltage model, 
- 
-\[ 
-\begin{align*} 
-U_{\rm D}\approx U_{\rm TO}. 
-\end{align*} 
-\] 
- 
-Therefore 
- 
-\[ 
-\begin{align*} 
-I_{\rm D} 
-\approx 
-\frac{U_{\rm E}-U_{\rm TO}}{R}. 
-\end{align*} 
-\] 
- 
-<callout type="danger" icon="true"> 
-Never connect a normal diode or LED directly to an ideal voltage source in forward direction.   
-The diode current must be limited. 
-</callout> 
- 
-==== Z-diodes and LEDs as diode types ==== 
- 
-A Z-diode is operated in reverse breakdown. In its operating range, the diode voltage is approximately constant: 
- 
-\[ 
-\begin{align*} 
-u_{\rm Z}\approx U_{\rm Z}. 
-\end{align*} 
-\] 
- 
-The piecewise-linear model is 
- 
-\[ 
-\begin{align*} 
-u_{\rm Z} 
-\approx 
-U_{\rm Z}+r_{\rm Z}i_{\rm Z}. 
-\end{align*} 
-\] 
- 
-<panel type="info" title="Z-diode preview"> 
-Z-diodes are useful for voltage limitation and voltage stabilization.   
-The practical circuits are treated in [[block12|Block 12]]. 
-</panel> 
- 
-An LED is a diode that emits light in forward direction. The required forward voltage depends on the semiconductor material and therefore on the color. 
- 
-<tabcaption tab_led_forward_voltage|Typical LED forward voltages> 
- 
-^ LED color ^ Typical \(U_{\rm TO}\) ^ 
-| infrared | \(\approx 1.3~{\rm V}\) | 
-| red | \(\approx 1.6~{\rm V}\) | 
-| yellow | \(\approx 1.7~{\rm V}\) | 
-| green | \(\approx 1.8~{\rm V}\) | 
-| blue | \(\approx 3.2~{\rm V}\) | 
- 
-<callout type="warning" icon="true"> 
-LEDs usually tolerate only small reverse voltages.   
-Do not operate an LED in reverse direction unless the datasheet explicitly allows it. 
-</callout> 
- 
-~~PAGEBREAK~~ ~~CLEARFIX~~ 
  
 ===== 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.
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 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}
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}=12~{\rm V},+U_{\rm I}=12~{\rm V},
 \qquad \qquad
 R=560~\Omega. R=560~\Omega.
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}+U_{\rm I}
 = =
 RI_{\rm D} RI_{\rm D}
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm E}+U_{\rm I}
 = =
 RI_{\rm D} RI_{\rm D}
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 I_{\rm D} I_{\rm D}
 = =
-\frac{U_{\rm E}-U_{\rm TO}}{R+r_{\rm F}}.+\frac{U_{\rm I}-U_{\rm TO}}{R+r_{\rm F}}.
 \end{align*} \end{align*}
 \] \]
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 ===== 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~~