Differences

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

--- electrical_engineering_and_electronics_2:block13 [2026/06/09 04:38] – mexleadmin
+++ electrical_engineering_and_electronics_2:block13 [2026/06/09 05:22] (current) – mexleadmin
@@ Line 1: / Line 1: @@
-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>
@@ Line 334: / Line 323: @@
 This is treated in [[block14|Block 14]].
 </callout>
-<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjA7CAMB00OgVnLJA2ALAJnQZjAA5DMjDJsR0xwQlo6BTAWjDACgBzEbYkPbA16F+edDBjsiNYeEyYefMAE5KDTPRKFYYiEjzIweQijiIacC-ARXz7AEqKRYeU-C8JDenU8w07AA8eZRRsTHEDKDDlEAUiEABhQJ4kKPRKXBjcFDiRACF2ABcU8WwIDL4ytVpmbB0ITGh0VTw8ZWUICAI-dF6kZWhsPAgiDvkYsAQQABNGADMAQwBXABtC9gAndxEqnmgd8olJhHYAdzcBIUq+aDO3bAw3FTV2ADdwMEpLj4zDhjxYgw4OI4Aogf5zmwvoILjDbpDPjxDp8Di8gthlKV2vx9jjKLkQABRZIuHZIShEAEPHLgET2AD6BUaALEznQXlU-Dh4HpD3Q9Lw9JwhGU9KQLDA-MIEog9OgvPp-LwyUwyhokpEqvEkBoBIAkskkIQogI6JyhjT4gagqqUJBxPQoJAYgSkkF+hlGlRoAowgCCUzoACsAxJQxCFguUCQKKkJ85ULJWAxSwwinavzk9h6aLlUFOurDhAQuA9LFaSA8sT8-1wL0QAW6y6KwBVZImUpiEARnZtcvxApBEwZDwmE26ivWngeXhCHCKf08BQAPjuglRJSRaOnO3wS6E9YDyWwQxSoRnRv7IinvBHMmUvrC5afr2PzR4LkUMkgV8Sb9CTRIkI0DNlax6YFABihOgkG4goXqAMmEx5sHi04ssgv5tuip4GDsEH8ChAbVlQhAUl2hDDOAfb6gAdgADkshQADoAM4JAAFgsGwLAAxoUjAbAAlixhSCTxyTDOqeAoEaEzGL+CRLBsGyMDRzEsQA4gsgk0axHFcbx-FCSJYnsAA9j4caUOIjQdD4cAiKG7BAA noborder}}
-</WRAP>
 ==== BJT characteristic curves and differential quantities ====
@@ Line 347: / Line 333: @@
   * **Control characteristic:** \(I_{\rm C}(I_{\rm B})\)  \\     This shows the current gain.
   * **Output characteristic:** \(I_{\rm C}(U_{\rm CE})\) for different values of \(I_{\rm B}\).
+<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=DwYwlgTgBAZgvAIgIwHYFQC4GdEAYB0uRuArOmCIkviQGwAsATLQMxIAc79H7qj6IAEaJaSdAAdhCErnQA3CFXQBbbIhIBTALRIxAPgBQUKMADmUAB6JGnKC0a4oN9nZa108BLID0h48AAZAENlcUtrWyR6eidIgE5+WDx0DA1rFiI4uJoWenYWEhl6VnQAO3E8QiIxKFK5SpqAdyDK4hqQAHtW6oRfIxMAJXCEZygomNGkGw9kqEbPWShlIIt66V6-EwthxjiSJ2K7XBQDuJmEenQsMCp2FLSEAGEN-uBtqxGSE+ZGJ1o4v5kJIXK43ZB3TAPABCL38GB2dCcKF+o0YyPOi3EpSUUEEDyQRBUXQQABMNDAggBXAA2GHkeMQWkY+BYKHouH+jBYLCyKBQbHplC8+FoopIcVwXJQHDibPoZz6-mgHymLjRKNwavRwMWimQxFhJkaO1s9kcqM4GMNwGNH1RiMmCStipMcmGul+ZrGUyRiQW6HmiBYHj17JUKzWBHcuLAQRwwsuLpt7p9XtGZudm2TKp96rGNl9mde72scVoTiyRxcGT9iEuUGut3uiAAotaS8g8k4SL8OCxu0DPPXG+DmwgBgB9GFJgDKnXEGmGbhcSFojnFnocVs2-g6UA02OQVwqn2jngsIBqJ50CB3xhMYTWwYbQvY2lQhvvD-3InkQaur7vmgLr+N4HRZt4c4dAuWYdvKSBjLQLjyuWqA1EOoJNpCiAAJLtsMJDsN89hQBuTgFOcw5ghwY54UmcF7GMKDljIJyoGcwJUVhqSIM89EEQkByOGuEz0M+GENtREI8Qg05ZlBC7DAwjiro47AMHYW46re-S7vuh4cVgJ4kFM5wWNwEiMvoun3sAj6zFgQqaEyiZ3v49kIM+jnqNozCfiYYEQQpGiwcMfIIXwUAoIxqCDnWmGjthsltvxHwoOKiHluFiEcRJI40UlACq+EfOwDpuFA6lqjylEJQVMlycWwxlSiBZlcR6HxZJ3EPHRoV2gWNjmkwsTiV1I6MPWMkAGSmBgADc1q2tYmq+t25bqkW-gdowg2sEJfxnuNUljo1207FyA5OINhG1d1iUyX1TV2uwrUIbsEyTXdE1TQ8cgldY-xOFEsTvR+nF1dJDx8f1gP7A4G0oOauC5cdPW4QDIz0CcGTw7QOOat9YJhklgDJhJjjC6EcrX9rjRPowgxWpdYl0ZGq2N2Lo9MPdCKWwwgSG9hV+RsTVEP3fVvXlJS8KPAAFkEEBBCAqQQGAWAYBQmOshFBSkdEYwsBCeUnUljwdKUGAQB01JQPLivK6r6uayA1p7ge6jHuopnAhYV7JHedlQGs0beesSaBQYwDeOAECGEAA noborder}}
+</WRAP>
+{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=DwYwlgTgBAZgvAIgIwHYFQC4GdEAYB0uRuATOmCIiYbgBwCs9AzAGwCcJTStKLaUIAEaIWSdAAdhCernQA3CIjFQAttkT0ApgFokYgHwAoKFGABzKAA8lLXFCYk7SW-dbp4CWQHojJ4ACUrGycAFhCoZycSWnc8dAB3DyZ3RQRaWVUAQ0s5JXRBMEycZAQfY1NLIOQWWigSFhII9LqWeliEEPQsMCUYzE1EAGFS3wqqpBI2FsakEKQWtthETqhu3vQMAYQAIRHy4Axx6LqUGZcSU-aM8QA7PKhBLaQidBUAe0QAE00YTIBXAA2GHkj0Qunwyjkgkonj2fmg1gQDhOMwmKKu6FSzxeZT88XGLgcTkJuBWHm8o2A+MRkTqIWJTg4GNxpjkVV0LHsjigHPRS1hUESVBSywyKmyuU8hDID0KxQILBYcNM1LBzi5DI1zMplRpNTqbCm3DsTFI7RWa2QfU2iAAosrgLrlig6vR5rRGiR6GTll0elaNlt-AB9XYsx3jOh1ZoTT20ZL8i3+kgrG0IABkZgwAG4HarkGiLjNjkXtfsnchcJyvUbuNNzX71v1EGGdZH5l75s9q96G6t-dxA4gAJIOitIb11EhdxVTn0dRsIFNDhByMfjOZ1WYRZhb-geJNNtPDcPjpguxyc2ae3BsPuWwfNhCj8MAZRAb3Emiq09qE7srSckw9AyuSCCjH4bxQJodwLqs4hKKQ86WCECYIQgujgeUJh+OIUCSkqqwwkg+BaNoMQsjhph4ZKMpYMROgURBpheG8lJeO+n6aJSbKIryRY8uqJDLvyGRCkuIpLmKEp4IQnThvm-Eplyc5lniVTIsJ4SaZconroifAdigtTsNWtDKAei6Pse9qnlUrRTPUUyGXyln9keWwAKr6cs54REwtRhDMcz3gO1pbC+baImEXYhJyIS7rMd6JlZ4VDD50h6BEfBQCwCURCgGRuQ+Mppp5VEmHAUCnLgKgAGoADRQMOOFVYVgA9wAAghlIEzCg4TMH+KD7r67nIKVWzbLZUUaGwHakLlDR1LgizFQOE0iOk9VNQlXUZQ0djCfQuVzVOfRrUoG0IHltWNXUTB7XZBlMOEnBTIVjkhKBo0lSuti3U1tANfQj2UgAMpkKh4XqoThLSSBMnpT7pKa+ANGw9BsEw2OKugNzoQQxATHjkoEMo8SZLJRPoB+VNEGI4aCFUqEus4gXnDIaljNF3L1C6ISFdGq0-etK5YJkGB-BAEtgG8NwADo3BAmhmLLNwOkz0WiHSJklpzelPcsbDVjlIGOQwoWXSuIB-BgbwwDA2iK8rqty3mBKHfS2WHfQhFgQpHvRn+JLzhS5Y-gtFy1NOr3mZbAZPt5htLtu0QXkwjlsEVIseUM03hzSDDRq9K3RiNcGWvSK6AMmEGW0EBpJQGwtSmuXh4J2VGXN-YzwRMJPcJhdHeTfnfjjtO9i4Kzm5cNnFf+lXT618nmNDeEthXsN8fE0+rYF4grBdreUDME4O9D9ZWwAPK2+IttQIMAAWmTSyAmwQGAWAYBQDpQTBGhdHQm6b6CBLCOFwMoAmWEqLABonEIidMIEOlYkYYAXhwAQCMEAA noborder}}
 Important parameters around an operating point are
@@ Line 365: / Line 357: @@
 \end{align*}
 \]
-<panel type="info" title="Simulation: BJT output characteristics">
-Things to try:
-  * change the input voltage \(U_{\rm BE}\),
-  * observe the family of output curves,
-  * identify cutoff, active region, and saturation.
-{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjA7CAMB00OgJhE+0AcBWLBmAbAJxK5gYT5T5jghbR0CmAtGGAFADm4+DuSDMLxC4CMGOwBKPQQBZZM8EgzjcIDINoM4WdgA8eKpPhRkGxrCAVkQAYX1LCqE+Fk0LV8CoBC7AC5KRhCmwkjB4jSssDSCCCAAJowAZgCGAK4ANn7sAE4iKGGmYAXhsQjsAO6K-ILCuNAK0JWKSLK1gsQSAG4grPj5DH2opahW2vAocPj947pVQzXVAhIGQkaETmYiyJ42AKIOslBIWDQYBVgK1iqSAPq+q5ioGkoFGGoKrSAAfM1sJaZlMNJg4wNB+idNjZjChriAHuBoO5ToiIZddioAJKg9FIJA0IQQr6fBRdUFuVBgax4SlQOH2Va4Y7g1wFaBOOHYtpqfEqMD0ED4LD9XBYSZWW5g1q3fC3Nz4XCS2BYFgYSWq27QW5IOXa9g9IaFXpCVBfcyocYNcSzZqGr78U2NZoOvEKF2lByUdwQFRECEYGj0g4GIVOYxOL3AjEgACqhyZ4FwKnkpgpnMOFKp-VkNKpHK8dgcpwJlEFOfAEAY1hQMYAOgBnBtNxst2sARwbwWgAFsAGoAGgbmObTY79crgB7gACCRbxFYUeD5EDpSnhwbohHcO2mbMs1cFGj7g-rOennuWeMsRHcQP3+DaR4bJDPIdwn1wTkrYdksNXvB7A4Nhg-ZYGeZAlnI1jCGAnQMBs-IwOgSKTNEiGIDESEcAARlYCZrFYoQCk0Bg-uYpZHG8e6rvWKR+GkOS0QAlgA9gAdrWtasTkjCcCxrHsDhsjUKgsi+kCJzaIchAQqWYphtguwoAAxmkfjMUkSTMBxXE8XxfyhG0LTChIVRCOYGB8nUVrERaJRGFSzyBgWcYGPinzkKgH6oIQVYFrY65kJYyifNAQUeVcDCAMmEDgYCKVqECo9QrjYLkgAlIhgq8GUfAW3gBfi2xQFSNCkL5hnRQYWDpZACi8P0kDJSgCL8PVxRWB5bBUTYzGqQADqpDZKQAFikDFKX4jA5Ix9Z+IxSnsMxdB0G1gh4hgThwOhaEIDE4DsEAA 700,500 noborder}}
-</panel>
 ~~PAGEBREAK~~ ~~CLEARFIX~~
 ==== 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>
-^ 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>
+\\
+=== Switching view ===
-<panel type="info" title="Switching view">
 For a BJT used as a switch:
@@ Line 404: / Line 385: @@
 \end{align*}
 \]
-</panel>
 The conduction loss of a saturated BJT switch is approximately
@@ Line 430: / Line 410: @@
 </callout>
-==== Switching times of a BJT ====
+=== Switching times of a BJT ===
 Real transistor switching is not instantaneous.
+{{drawio>electrical_engineering_and_electronics_2:switchingdiagram_v01.svg}}
 Typical time intervals are:
@@ Line 438: / Line 420: @@
 <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>
+\\
-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.
 \[
 \begin{align*}
-p(t)=u_{\rm CE}(t)i_{\rm C}(t).
+p(t)=u_{\rm CE}(t) \cdot i_{\rm C}(t).
 \end{align*}
 \]
@@ Line 461: / Line 443: @@
 This contributes to the storage time \(t_{\rm s}\).
 </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~~
@@ Line 559: / Line 501: @@
 </panel>
 </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 ====
@@ Line 594: / Line 526: @@
 \(U_{\rm GS(th)}\) 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>
 </WRAP>
@@ Line 625: / Line 551: @@
 ~~PAGEBREAK~~ ~~CLEARFIX~~
 ==== 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>
-^ 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>
+\\
 <callout type="warning" icon="true">
 The word **saturation** means different things for BJTs and MOSFETs.
@@ Line 663: / Line 589: @@
 \[
 \begin{align*}
-U_{\rm DS}\approx R_{\rm DS(on)}I_{\rm D}.
+U_{\rm DS}\approx R_{\rm DS(on)} \cdot I_{\rm D}.
 \end{align*}
 \]
@@ Line 674: / Line 600: @@
 P_{\rm on,MOS}
 =
-R_{\rm DS(on)}I_{\rm D}^2
+R_{\rm DS(on)} \cdot I_{\rm D}^2
 }
 \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 ====
@@ Line 719: / Line 619: @@
 <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>
+\\
 In many mechatronic power circuits, the most common device is the **n-channel enhancement MOSFET**.
@@ Line 730: / Line 630: @@
 <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>
 <callout type="warning" icon="true">
 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>