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electrical_engineering_and_electronics_2:block13 [2026/06/09 04:17] – 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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 The arrow indicates the technical current direction at the emitter in normal operation. The arrow indicates the technical current direction at the emitter in normal operation.
 </callout> </callout>
 +
 +<WRAP>
 +{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=DwYwlgTgBAZgvAIgIwHYFQC4GdEAYB0uRuArOmCIkviQGwAsATLQMxIAc79H7qj6IAEaJaSdAAdhCErnQA3CFXQBbbIhIBTALRIxAPgBQUKMADmUAB6JGnKDfZ3bLXPXTwEsgPSHjwaFeQbO3pcO1wHRhC3PHRFZGIEbyMTAHdLa1t7RwiUflgYpN85dOQkRmyoXXLI2XyPdBT3WuUAQws5PHx2RJ9UkqqKrPto+sK+gIGayqCaka9e4At++gjGUI4WO0YWEdcoLDAqbswNRAAlAH0AIR7k4DSAtYiQuzpg2qbb30ES9lCATloUBYJHowLWcy+JiWAX+SCgJGqXCg7Dy7j2B2sewwpwQAB0AHYtAkYMDiFoQFoAGypGipUAAJmAAPYMjRYKGLEosP4ooGiIHsf67dCYhCRdA4xAAOQACtKtIIycyqRTMJSCQcsBhmRBOT8AixaA5AVAGOUWBC6vM7jD1ChQmt-gjUXYyiL9odxdjcXJOQ9EPRTVNQWDZtbOXbpEggZEHCRnK8xHUMV6JSdEAAyUwYADckZK9CNW1C9BQ8MY2w9Yo4ktxlxuY3uhaI7yg3FjUQjTYDCBCjtsJBQsc4kKbxQC-YqU-DnygjRiUFa7U63R7JSHsciCOHlX+aIKC17m4qJ8YdDHC38gZjbaDnY+i7iSASTYwG-oYZeZ67c-EBKUKBBFxF9mmZRA2RgFoAFcqQweRgMQLRGHwAUUEROhwhQS0UHYMgoDkQRKA8VDWErcIg1IJgEzXBYzg3XckE-HcgSqSF5znZcOmkTkABkWmUcQGNY5iTyQfd2KlBA2ErdhaHwFAyyINZSBYPYCXETpiGTAluIIZMUhaLSiGTEBwJI7TOXMAIz0HXdnD2T4mwZEohheIZchGPJlHMyCYLg-1XLeKY3MfUYFhcx5MnczJwi8lRfI0KDYPgpt+ME1zbCYsMsokiMM2kohCGIXBxJWbDaFoNAoA04zSvQXTOgMoyLJMgRzIISym3oqKHGyio2Pyhd6iXNpuLIdderCCJcoPcKDGATxwAgQwgA noborder}}
 +</WRAP>
  
 <panel type="info" title="Important limitation of the diode picture"> <panel type="info" title="Important limitation of the diode picture">
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 ==== How the npn transistor controls current ==== ==== How the npn transistor controls current ====
  
 +<WRAP left>
 +<panel type="default">
 +<imgcaption fig_bjt_function|Simplified function of an npn bipolar junction transistor: base current enables collector current.></imgcaption>
 +{{:circuit_design:funktion_des_bipolartransistor2.svg?650}}
 +</panel>
 +</WRAP>
 +
 +Here, the figures in <imgref fig_bjt_function> shall be described:
 +  - Figure: The physics of controlling the BJT takes place in the narrow P-layer in the middle. \\ The following figures 2. - 6. refer to the highlighted section.
 +  - Figure - Situation $U_{\rm CE}=0~{\rm V}, U_{\rm BE}=0 ~\rm V$: \\ In this picture the unpowered transistor is shown. In it the free charge carriers (electrons in green, holes in red) and the junction layers between base and emitter, and base and collector in yellow. Only the junction layer shows the stationary charge carriers with their sign. As shown in the band model, the stationary charge carriers are present everywhere in both doped regions. \\ \\
 +  - Figure - Situation $U_{\rm CE}=0~{\rm V}, 0~{\rm V}<U_{\rm BE}<0.6~\rm V$: \\ First, consider a small, positive voltage $U_{\rm BE}$. This provides holes in the base with current $I_\rm B$. This operates the PN junction between the base and emitter in the forward direction. In the figure, it is indicated with black circles that the injected holes compensate some stationary negative charge carriers in both junction layers. Electrons also flow through the emitter into the n-region, which attenuates the junction on the other side.
 +  - Figure - Situation $U_{\rm CE}=0~{\rm V}, U_{\rm BE}>0.6 \rm V$: \\ When the forward voltage of the PN junction between the base and emitter is exceeded, the injected holes and electrons cancel the bottom junction. In the simulation below, it can be seen that the circuitry of the transistor is such that in the diode circuit (which is not physically correct), the diode between the base and emitter becomes conductive. \\ \\
 +  - Figure - Situation $U_{\rm CE}>0~{\rm V}, U_{\rm BE}>0.6~\rm V$: \\ Now with this voltage at the base, the working circuit, i.e. a voltage $U_{\rm BE}>0$ should be present at the output. In the real system, the base is very small compared to the mean free path length of the electrons ("path to recombination with a hole"). This changes the situation at the upper PN junction. In a classical diode, no electrons are present in the P-doped region. However, the electrons present here can cross the base and compensate for the stationary positive charge carriers in the upper junction. The holes injected into the base in turn compensate for the stationary negative charge carriers. Thus, this junction layer is also removed. This is possible as long as enough holes are injected into the base.
 +  - Figure - Situation $U_{\rm CE}>0~{\rm V}, U_{\rm BE}>0.6~\rm V$: \\ Thus, in the NPN bipolar junction transistor, both holes (to remove the junction layers) and electrons (as the "main agents" responsible for charge transport, the so-called majority carrier charges) contribute to the conductivity. This is where the name __bipolar__ junction transistor comes from.
 +
 +~~PAGEBREAK~~ ~~CLEARFIX~~
 +
 +<panel type="info" title="TLDR: How a transistor works">
 The base-emitter junction behaves approximately like a diode.   The base-emitter junction behaves approximately like a diode.  
 For a silicon transistor, noticeable base current often starts around For a silicon transistor, noticeable base current often starts around
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 \] \]
  
-When enough base current flows, the thin base region allows many carriers to pass from emitter to collector. Thus a small base current can control a larger collector current.+When enough base current flows, the thin base region allows many carriers to pass from emitter to collector.  
 +Thus a small base current can control a larger collector current.
  
-<WRAP> +Because both electrons and holes contribute to the physical operation, the component is called **bipolar**.
-<panel type="default"> +
-<imgcaption fig_bjt_function|Simplified function of an npn bipolar junction transistor: base current enables collector current.></imgcaption> +
-{{:circuit_design:funktion_des_bipolartransistor2.svg?650}}+
 </panel> </panel>
-</WRAP> 
  
-<panel type="info" title="Analogy: narrow gate in a hallway"> 
-Imagine many people want to move from a large entrance hall to an exit hall, but a narrow gate is blocked. 
- 
-  * The emitter is the entrance side. 
-  * The collector is the exit side. 
-  * The base is the small gate control region. 
- 
-A small action at the gate can allow many people to pass through the main hallway.   
-This is only an analogy, but it helps to remember: the base controls a much larger collector-emitter current. 
-</panel> 
- 
-Because both electrons and holes contribute to the physical operation, the component is called **bipolar**. 
  
 <callout> <callout>
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 </callout> </callout>
  
-~~PAGEBREAK~~ ~~CLEARFIX~~+==== Current gain of the BJT ====
  
-==== Current gain of the BJT ====+In the active region, a small base current controls a larger collector current. The base current flows over a diode between base and emitter (depict as arrot in the symbol).
  
-In the active region, a small base current controls a larger collector current.+<WRAP><imgcaption picJ|function of NPN bipolar junction transistor> 
 +{{elektronische_schaltungstechnik:jbt_funktionsweise.jpg?400}} 
 +</imgcaption></WRAP>
  
 \[ \[
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 \[ \[
 \begin{align*} \begin{align*}
-\beta+h_{\rm FE} = \beta
 = =
 \frac{\Delta I_{\rm C}}{\Delta I_{\rm B}} \frac{\Delta I_{\rm C}}{\Delta I_{\rm B}}
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 This is treated in [[block14|Block 14]]. This is treated in [[block14|Block 14]].
 </callout> </callout>
- 
-<panel type="info" title="Simulation: input and current-gain characteristics"> 
-Things to try: 
- 
-  * change \(U_{\rm BE}\), 
-  * observe how \(I_{\rm B}\) changes, 
-  * observe how \(I_{\rm C}\) changes with \(I_{\rm B}\). 
- 
-{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjA7CAMB00OgVnLJA2ALAJnQZjAA5DMjDJsR0xwQlo6BTAWjDACgBzEbYkPbA16F+edDBjsiNYeEyYefMAE5KDTPRKFYYiEjzIweQijiIacC-ARXz7AEqKRYeU-C8JDenU8w07AA8eZRRsTHEDKDDlEAUiEABhQJ4kKPRKXBjcFDiRACF2ABcU8WwIDL4ytVpmbB0ITGh0VTw8ZWUICAI-dF6kZWhsPAgiDvkYsAQQABNGADMAQwBXABtC9gAndxEqnmgd8olJhHYAdzcBIUq+aDO3bAw3FTV2ADdwMEpLj4zDhjxYgw4OI4Aogf5zmwvoILjDbpDPjxDp8Di8gthlKV2vx9jjKLkQABRZIuHZIShEAEPHLgET2AD6BUaALEznQXlU-Dh4HpD3Q9Lw9JwhGU9KQLDA-MIEog9OgvPp-LwyUwyhokpEqvEkBoBIAkskkIQogI6JyhjT4gagqqUJBxPQoJAYgSkkF+hlGlRoAowgCCUzoACsAxJQxCFguUCQKKkJ85ULJWAxSwwinavzk9h6aLlUFOurDhAQuA9LFaSA8sT8-1wL0QAW6y6KwBVZImUpiEARnZtcvxApBEwZDwmE26ivWngeXhCHCKf08BQAPjuglJSRaOnO3wS6E9YDyWwQxSoRnRv7IinvBHMmUvrC5afr2PzR4LkUMkgV8Sb9CTRIkI0DNlax6YFABihOgkG4goXqAMmEx5sHi04ssgv5tuip4GDsEH8ChAbVlQhAUl2hDDOAfb6gAdgADkshQADoAM4JAAFgsGwLAAxoUjAbAAlixhSCTxyTDOqeAoEaEzGL+CRLBsGyMDRzEsQA4gsgk0axHFcbx-FCSJYnsAA9j4caUOIjQdD4cAiKG7BAA 700,500 noborder}} 
-</panel> 
  
 ==== BJT characteristic curves and differential quantities ==== ==== BJT characteristic curves and differential quantities ====
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 Important BJT characteristics are: Important BJT characteristics are:
  
-  * **Input characteristic:** \(I_{\rm B}(U_{\rm BE})\)   +  * **Input characteristic:** \(I_{\rm B}(U_{\rm BE})\)  \\     The base-emitter path behaves approximately like a diode. 
-    The base-emitter path behaves approximately like a diode. +  * **Control characteristic:** \(I_{\rm C}(I_{\rm B})\)  \\     This shows the current gain.
-  * **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 \(I_{\rm B}\).   * **Output characteristic:** \(I_{\rm C}(U_{\rm CE})\) for different values of \(I_{\rm B}\).
  
-<WRAP> + 
-<panel type="default"> +<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}}
-<imgcaption fig_bjt_characteristics|Input, control, and output characteristics of an npn transistor.></imgcaption> +
-{{drawio>block13_bjt_characteristics.svg}} +
-</panel>+
 </WRAP> </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 Important parameters around an operating point are
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 \end{align*} \end{align*}
 \] \]
- 
-<callout type="info" icon="true"> 
-**Unit check** 
- 
-\[ 
-\begin{align*} 
-[r_{\rm BE}] 
-= 
-\frac{{\rm V}}{{\rm A}} 
-= 
-\Omega, 
-\qquad 
-[r_{\rm CE}] 
-= 
-\frac{{\rm V}}{{\rm A}} 
-= 
-\Omega. 
-\end{align*} 
-</callout> 
- 
-<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~~ ~~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
Line 455: Line 410:
 </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:
Line 463: Line 420:
 <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.
  
 \[ \[
 \begin{align*} \begin{align*}
-p(t)=u_{\rm CE}(t)i_{\rm C}(t).+p(t)=u_{\rm CE}(t) \cdot i_{\rm C}(t).
 \end{align*} \end{align*}
 \] \]
Line 486: Line 443:
 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~~
Line 584: Line 501:
 </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 ====
Line 619: Line 526:
 \(U_{\rm GS(th)}\) 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>
Line 650: Line 551:
  
 ~~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.
Line 688: Line 589:
 \[ \[
 \begin{align*} \begin{align*}
-U_{\rm DS}\approx R_{\rm DS(on)}I_{\rm D}.+U_{\rm DS}\approx R_{\rm DS(on)} \cdot I_{\rm D}.
 \end{align*} \end{align*}
 \] \]
Line 699: Line 600:
 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 ====
Line 744: Line 619:
 <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**.
  
Line 755: Line 630:
 <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>