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electrical_engineering_and_electronics_2:block13 [2026/06/09 04:41] – mexleadminelectrical_engineering_and_electronics_2:block13 [2026/06/09 05:22] (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]] ) 
- 
-    - 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 
- 
- 
- 
 <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> <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>
  
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 \end{align*} \end{align*}
 \] \]
- 
- 
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
- 
 ==== BJT operating regions ==== ==== BJT operating regions ====
  
-A BJT can operate in different regions.+A BJT operates mainly in three different regions.
  
 <tabcaption tab_bjt_regions|Basic operating regions of an npn transistor> <tabcaption tab_bjt_regions|Basic operating regions of an npn transistor>
  
-^ Region ^ Approximate condition ^ Electrical behavior ^ Typical use ^ +^ Region         ^ Approximate condition ^ Electrical behavior ^ Typical use ^ 
-| cutoff | \(I_{\rm B}\approx 0\) | \(I_{\rm C}\approx 0\), transistor blocks | open switch | +| cutoff         | \(I_{\rm B}\approx 0\)                            | \(I_{\rm C}\approx 0\), transistor blocks     | open switch       | 
-| active region | \(I_{\rm C}\approx B I_{\rm B}\) | collector current controlled by base current | analog amplifier | +| active region  | \(I_{\rm C}\approx B I_{\rm B}\)                  | collector current controlled by base current  | analog amplifier  | 
-| saturation | \(I_{\rm B}\) large enough, \(U_{\rm CE}\) small | transistor conducts strongly | closed switch |+| saturation     | \(I_{\rm B}\) large enough, \\ \(U_{\rm CE}\) small  | transistor conducts strongly                  | closed switch     |
 </tabcaption> </tabcaption>
 +\\ 
 +=== Switching view ===
  
-<panel type="info" title="Switching view"> 
 For a BJT used as a switch: For a BJT used as a switch:
  
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 \end{align*} \end{align*}
 \] \]
-</panel> 
  
 The conduction loss of a saturated BJT switch is approximately The conduction loss of a saturated BJT switch is approximately
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 </callout> </callout>
  
-==== Switching times of a BJT ====+=== Switching times of a BJT ===
  
 Real transistor switching is not instantaneous. Real transistor switching is not instantaneous.
 +
 +{{drawio>electrical_engineering_and_electronics_2:switchingdiagram_v01.svg}}
  
 Typical time intervals are: Typical time intervals are:
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 <tabcaption tab_bjt_switching_times|BJT switching times> <tabcaption tab_bjt_switching_times|BJT switching times>
  
-^ Symbol ^ Meaning ^ +^ Symbol           ^ Meaning  ^ 
-| \(t_{\rm d}\) | delay time | +| \(t_{\rm d}\)    | delay time           | 
-| \(t_{\rm r}\) | rise time | +| \(t_{\rm r}\)    | rise time            | 
-| \(t_{\rm on}\) | total turn-on time | +| \(t_{\rm on}\)   | total turn-on time   | 
-| \(t_{\rm s}\) | storage time | +| \(t_{\rm s}\)    | storage time         | 
-| \(t_{\rm f}\) | fall time | +| \(t_{\rm f}\)    | fall time            | 
-| \(t_{\rm off}\) | total turn-off time |+| \(t_{\rm off}\)  | total turn-off time  |
 </tabcaption> </tabcaption>
- +\\ 
-During switching, both current and voltage can be significant at the same time.  +During switching, both current and voltage can be significant at the same time.  \\
 Therefore switching losses occur during turn-on and turn-off. Therefore switching losses occur during turn-on and turn-off.
  
 \[ \[
 \begin{align*} \begin{align*}
-p(t)=u_{\rm CE}(t)i_{\rm C}(t).+p(t)=u_{\rm CE}(t) \cdot i_{\rm C}(t).
 \end{align*} \end{align*}
 \] \]
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 This contributes to the storage time \(t_{\rm s}\). This contributes to the storage time \(t_{\rm s}\).
 </panel> </panel>
- 
-==== Short preview: transistor switch and PWM ==== 
- 
-A transistor switch can connect and disconnect a load very quickly.   
-If the switch is periodically on and off, the load sees an average voltage. 
- 
-For an ideal switch with supply voltage \(U_{\rm dc}\): 
- 
-\[ 
-\begin{align*} 
-\overline{u}_{\rm L} 
-= 
-\frac{1}{T}\int_0^T u_{\rm L}(t)\,{\rm d}t 
-= 
-\frac{T_{\rm on}}{T}U_{\rm dc}. 
-\end{align*} 
-\] 
- 
-The duty cycle is 
- 
-\[ 
-\begin{align*} 
-d=\frac{T_{\rm on}}{T}. 
-\end{align*} 
-\] 
- 
-Thus 
- 
-\[ 
-\begin{align*} 
-\boxed{ 
-\overline{u}_{\rm L}=dU_{\rm dc} 
-} 
-\end{align*} 
-\] 
- 
-<callout> 
-This is the basic idea of pulse-width modulation (PWM).   
-Applications to motor drivers and power stages are continued in [[block14|Block 14]]. 
-</callout> 
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
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 </panel> </panel>
 </WRAP> </WRAP>
- 
-<panel type="info" title="Simulation: MOSFET as voltage-controlled switch"> 
-Things to try: 
- 
-  * change the gate voltage, 
-  * observe that the gate draws no stationary current, 
-  * observe how the drain-source path changes from blocking to conducting. 
- 
-{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjA7CAMB00OgJhE+0AcBWLBmAbAJxK5gYT5T5jghbR0CmAtGGAFADm4+DuSDMLxC4CMGOwBKPQQBZZM8EgzjcIDAzhq4KTbCzsAHuAhqkecNlRZ8IBWRAARI+CHX7uBuaj2VAcXYAJxEUJAgUNlDw8TBEdgB3RX5BYU8FaATFJFkUwWIJADcQkL4o3VQ7QVodJHwMYg0wrGJ8ZSwYfUz+EqSBCWNIBTTLW08fSxAAZUzI1GiwZTndFzAsBSQkGiFbDYV1hQKV2RpN+wtN8YdnAdwoAVswWVDoQjsJgEl2Mi3hR-tf-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-WnZi-knPZITsQhI2QWQc3jPMvXMOqwTTZgckjZNluRFhjhzPN6HDQtjDfKzQ3UdjXjNFwDIAkB8HaZgl3ZSQXEoawUG4m9iICED9lsE7skuiYXvvE7WDWEQIF01Y2Q+T8IBG2RRgwDTHlNCZrjobjmA2O7wSs8TjItGxXnMmgAN0xZ2S5IA 700,500 noborder}} 
-</panel> 
  
 ==== MOSFET structure and channel formation ==== ==== MOSFET structure and channel formation ====
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 \(U_{\rm GS(th)}\) is **not** the voltage for a fully switched-on MOSFET. \(U_{\rm GS(th)}\) is **not** the voltage for a fully switched-on MOSFET.
  
-For low conduction loss, use the gate voltage at which the datasheet specifies +For low conduction loss, use the gate voltage at which the datasheet specifies $R_{\rm DS(on)}$.
- +
-\[ +
-\begin{align*} +
-R_{\rm DS(on)}. +
-\end{align*} +
-\]+
 </panel> </panel>
 </WRAP> </WRAP>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
- 
 ==== MOSFET output characteristics ==== ==== MOSFET output characteristics ====
  
-The drain current \(I_{\rm D}\) depends on+The drain current $I_{\rm D}$ depends on 
 +  * the drain-source voltage $U_{\rm DS}$, and 
 +  * the gate-source voltage $U_{\rm GS}$. 
  
-  * the drain-source voltage \(U_{\rm DS}\), +{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0lwTFa8CscCcAWOYDMA2feMedEfSEFETXKgUwFowwAoAM3E0xFwA4eYAOz5eA3ojDRqMSPFYAncCTGCVuAlHBxIrAObgRNXJKPc+W3WD4Rhok5Tu8UiR-AyVcTIUhy-IELIBrABuNBb8PJgRmpSI7kiBltKsAEqG9glO8HwWniB8juDJKKwA7sqIkVw81bph0caIjXUgzZSy1FJ5SKUVTrTNFoNQ5RlN49gdYyxVmi2xM0a4LuMEeazYdPBC8bvkkMP4PB0A+senkKeYYESnKEy3p2CPQpen8O+4rAAeBXQ3Sjoag3AHgCwAVV+IHQPkwWXgAMRNHBIAA4gBlaEkZq3Li4shRSiAZMJoShcD4cj58EJtuhKIJIQAdADOrPZbLZAEd2QAHMDAyCsgC2ADUyZgyKQeCghNRSHDUZiyXwyLhrOQhBATBBGSAmfz6UKWWKVREbprPNwURqDdY0CLxX8ULleBRLW6wbb+YVjabnTYxNQUOg6Pxhqioc70FVQ+RhLx0KI9QARLF-eFxIQM1BtWk2iwASWh8J4O0JmhyzVRWIARjRjm0Y1Q+NQCDJodUTADsLwLYJECyAIYAFwArgpRwBLAD2ADt2Uy5wp6HpZ3OSyhtUIyC4fPxqyoAMJjkesmfsdis1Kr9fYvj2OPuR-Jmgk6HENXoCDwa24LAFiAaYfnIYjxGAtStoBUYgMwZaYPuKDymgKK-iAc6MEeAAWQ5znO9AADasvQc44XOADG9DCiRZ4sgAsgA8hiABiACiAAqrBAA 700,500 noborder}}
-  * the gate-source voltage \(U_{\rm GS}\).+
  
-<WRAP> +\\ 
-<panel type="default"> +
-<imgcaption fig_mosfet_output_characteristic|Qualitative output characteristics of an n-channel enhancement MOSFET.></imgcaption> +
-{{drawio>block13_mosfet_output_characteristics.svg}} +
-</panel> +
-</WRAP>+
  
-A MOSFET has several operating regions. Their names can be confusing because they are not identical to the BJT names.+<WRAP><imgcaption picP|Function of the MOSFET> 
 +{{elektronische_schaltungstechnik:mosfet-front-final-test_jpg_project-body.jpg?400}} 
 +</imgcaption></WRAP> 
 + 
 +A MOSFET has several operating regions. \\ 
 +Their names can be confusing because they are not identical to the BJT names.
  
 <tabcaption tab_mosfet_regions|Basic regions of an n-channel enhancement MOSFET> <tabcaption tab_mosfet_regions|Basic regions of an n-channel enhancement MOSFET>
  
-^ Region ^ Approximate condition ^ Electrical behavior ^ Typical use ^ +^ Region                    ^ Approximate condition                       ^ Electrical behavior                          ^ Typical use     ^ 
-| cutoff | \(U_{\rm GS}<U_{\rm GS(th)}\) | no useful channel, \(I_{\rm D}\approx 0\) | open switch | +| cutoff                    | \(U_{\rm GS}<U_{\rm GS(th)}\)               | no useful channel, \(I_{\rm D}\approx 0\)    | open switch     | 
-| linear / ohmic region | \(U_{\rm GS}\) high, \(U_{\rm DS}\) small | behaves like a controlled resistor | closed switch | +| linear / ohmic region     | \(U_{\rm GS}\) high, \(U_{\rm DS}\) small   | behaves like a controlled resistor           | closed switch   | 
-| MOSFET saturation region | \(U_{\rm GS}\) high, \(U_{\rm DS}\) larger | current mainly controlled by \(U_{\rm GS}\) | analog operation, current-source-like behavior |+| MOSFET saturation region  | \(U_{\rm GS}\) high, \(U_{\rm DS}\) larger  | current mainly controlled by \(U_{\rm GS}\)  | analog operation, current-source-like behavior  |
 </tabcaption> </tabcaption>
 +\\ 
 <callout type="warning" icon="true"> <callout type="warning" icon="true">
 The word **saturation** means different things for BJTs and MOSFETs. The word **saturation** means different things for BJTs and MOSFETs.
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 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm DS}\approx R_{\rm DS(on)}I_{\rm D}.+U_{\rm DS}\approx R_{\rm DS(on)} \cdot I_{\rm D}.
 \end{align*} \end{align*}
 \] \]
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 P_{\rm on,MOS} P_{\rm on,MOS}
 = =
-R_{\rm DS(on)}I_{\rm D}^2+R_{\rm DS(on)} \cdot I_{\rm D}^2
 } }
 \end{align*} \end{align*}
 \] \]
  
-<callout type="info" icon="true"> 
-**Unit check** 
- 
-\[ 
-\begin{align*} 
-[P_{\rm on,MOS}] 
-= 
-\Omega\cdot{\rm A}^2 
-= 
-\frac{{\rm V}}{{\rm A}}\cdot{\rm A}^2 
-= 
-{\rm V\,A} 
-= 
-{\rm W}. 
-\end{align*} 
-</callout> 
- 
-<panel type="info" title="Simulation: MOSFET output characteristics"> 
-Things to try: 
- 
-  * change \(U_{\rm GS}\), 
-  * observe the family of output curves, 
-  * identify cutoff, linear/ohmic region, and MOSFET saturation region. 
- 
-{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0lwTFa8CscCcAWOYDMA2feMedEfSEFETXKgUwFowwAoAM3E0xFwA4eYAOz5eA3ojDRqMSPFYAncCTGCVuAlHBxIrAObgRNXJKPc+W3WD4Rhok5Tu8UiR-AyVcTIUhy-IELIBrABuNBb8PJgRmpSI7kiBltKsAEqG9glO8HwWniB8juDJKKwA7sqIkVw81bph0caIjXUgzZSy1FJ5SKUVTrTNFoNQ5RlN49gdYyxVmi2xM0a4LuMEeazYdPBC8bvkkMP4PB0A+senkKeYYESnKEy3p2CPQpen8O+4rAAeBXQ3Sjoag3AHgCwAVV+IHQPkwWXgAMRNHBIAA4gBlaEkZq3Li4shRSiAZMJoShcD4cj58EJtuhKIJIQAdADOrPZbLZAEd2QAHMDAyCsgC2ADUyZgyKQeCghNRSHDUZiyXwyLhrOQhBATBBGSAmfz6UKWWKVREbprPNwURqDdY0CLxX8ULleBRLW6wbb+YVjabnTYxNQUOg6Pxhqioc70FVQ+RhLx0KI9QARLF-eFxIQM1BtWk2iwASWh8J4O0JmhyzVRWIARjRjm0Y1Q+NQCDJodUTADsLwLYJECyAIYAFwArgpRwBLAD2ADt2Uy5wp6HpZ3OSyhtUIyC4fPxqyoAMJjkesmfsdis1Kr9fYvj2OPuR-Jmgk6HENXoCDwa24LAFiAaYfnIYjxGAtStoBUYgMwZaYPuKDymgKK-iAc6MEeAAWQ5znO9AADasvQc44XOADG9DCiRZ4sgAsgA8hiABiACiAAqrBAA 700,500 noborder}} 
-</panel> 
  
 ==== MOSFET types ==== ==== MOSFET types ====
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 <tabcaption tab_mosfet_types|Basic MOSFET types> <tabcaption tab_mosfet_types|Basic MOSFET types>
  
-^ Channel type ^ Enhancement type / self-blocking ^ Depletion type / self-conducting ^ +^ Channel type  ^ Enhancement type / self-blocking  ^ Depletion type / self-conducting  ^ 
-| n-channel | off at \(U_{\rm GS}=0\), on for sufficiently positive \(U_{\rm GS}\) | on at \(U_{\rm GS}=0\), can be reduced by negative \(U_{\rm GS}\) | +| n-channel  | off at \(U_{\rm GS}=0\), on for sufficiently positive \(U_{\rm GS}\)  | on at \(U_{\rm GS}=0\), can be reduced by negative \(U_{\rm GS}\)  | 
-| p-channel | off at \(U_{\rm GS}=0\), on for sufficiently negative \(U_{\rm GS}\) | on at \(U_{\rm GS}=0\), can be reduced by positive \(U_{\rm GS}\) |+| p-channel  | off at \(U_{\rm GS}=0\), on for sufficiently negative \(U_{\rm GS}\)  | on at \(U_{\rm GS}=0\), can be reduced by positive \(U_{\rm GS}\)  |
 </tabcaption> </tabcaption>
 +\\ 
 In many mechatronic power circuits, the most common device is the **n-channel enhancement MOSFET**. In many mechatronic power circuits, the most common device is the **n-channel enhancement MOSFET**.
  
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 <tabcaption tab_bjt_mosfet_comparison|BJT and MOSFET as switching elements> <tabcaption tab_bjt_mosfet_comparison|BJT and MOSFET as switching elements>
  
-^ Property ^ BJT ^ MOSFET ^ +^ Property                    ^ BJT  ^ MOSFET  ^ 
-| control quantity | base current \(I_{\rm B}\) | gate-source voltage \(U_{\rm GS}\) | +| control quantity            | base current \(I_{\rm B}\)                     | gate-source voltage \(U_{\rm GS}\)                                    | 
-| stationary control current | required | approximately zero | +| stationary control current  | required                                       | approximately zero                                                    | 
-| stationary control loss | \(P_{\rm ctrl}\approx U_{\rm BE}I_{\rm B}\) | very small, but gate must be charged and discharged during switching | +| stationary control loss     | \(P_{\rm ctrl}\approx U_{\rm BE}I_{\rm B}\)    | very small, but gate must be charged and discharged during switching  | 
-| on-state loss | \(P_{\rm on}\approx U_{\rm CE,sat}I_{\rm C}\) | \(P_{\rm on}=R_{\rm DS(on)}I_{\rm D}^2\) | +| on-state loss               | \(P_{\rm on}\approx U_{\rm CE,sat}I_{\rm C}\)  | \(P_{\rm on}=R_{\rm DS(on)}I_{\rm D}^2\)                              |  
-| switching behavior | storage charge can slow turn-off | often faster, but gate capacitance matters | +| switching behavior          | storage charge can slow turn-off               | often faster, but gate capacitance matters                            | 
-| typical risk | current gain \(B\) varies strongly | gate oxide sensitive to overvoltage and ESD |+| typical risk                | current gain \(B\) varies strongly             | gate oxide sensitive to overvoltage and ESD                           |
 </tabcaption> </tabcaption>
  
 <callout type="warning" icon="true"> <callout type="warning" icon="true">
 MOSFET gates are sensitive.   MOSFET gates are sensitive.  
-A too large \(|U_{\rm GS}|\) can destroy the thin gate oxide.+A too large \(|U_{\rm GS}|\) can destroy the thin gate oxide. \\
 </callout> </callout>