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--- electrical_engineering_and_electronics_2:block13 [2026/06/02 03:22] – mexleadmin
+++ electrical_engineering_and_electronics_2:block13 [2026/06/09 05:22] (current) – mexleadmin
@@ Line 1: / Line 1: @@
-TBD
+<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>
-  - Semiconductor components \\ (approx. 4 blocks, based on previous lectures on [[circuit_design:2_diodes|Diodes]] and [[circuit_design:2_transistors|Transistors]] )
+====== Block 13 — Transistor Fundamentals ======
-    - Bipolar transistor (structure, designations, characteristic curve, characteristic values)
+===== Learning objectives =====
-    - Transistor as a switch (circuit, switching times and behavior)
+<callout>
-    - MOSFET (structure, comparison with bipolar transistor)
+After this 90-minute block, you can
-    - Optional: Transistor as an amplifier
+  * explain why a transistor can act as a controlled electronic valve.
+  * distinguish bipolar junction transistors (BJTs) and field-effect transistors (FETs).
+  * identify the terminals of a BJT: base \(B\), collector \(C\), and emitter \(E\).
+  * distinguish npn and pnp bipolar transistors from their layer structure and circuit symbols.
+  * describe normal operation of an npn transistor using \(U_{\rm BE}\), \(U_{\rm CE}\), \(U_{\rm CB}\), \(I_{\rm B}\), \(I_{\rm C}\), and \(I_{\rm E}\).
+  * use the current-gain approximation
+\[
+\begin{align*}
+I_{\rm C}\approx B I_{\rm B}
+\end{align*}
+\]
+for simple operating-point estimates.
+  * identify the basic BJT operating regions: cutoff, active region, and saturation.
+  * explain why a saturated BJT is suitable as a closed switch, but not as a linear amplifier.
+  * identify the terminals of a MOSFET: gate \(G\), source \(S\), drain \(D\), and bulk \(B\).
+  * explain why a MOSFET is mainly voltage-controlled and why the stationary gate current is approximately zero.
+  * compare BJTs and MOSFETs as switching elements at a basic level.
+</callout>
+===== 90-minute plan =====
-<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>
+  * **Warm-up (10 min):**
+    * Where do transistors occur in a robot controller?
+    * Recall from [[block11|Block 11]]: pn junctions and diode behavior.
+    * Recall from [[block12|Block 12]]: diodes are useful, but they cannot actively control a load current.
+  * **Core concepts (55 min):**
+    * Introductory example: transistors inside logic circuits.
+    * Transistor as controlled valve: control circuit and load circuit.
+    * BJT terminals, npn/pnp structure, and sign conventions.
+    * BJT current gain, characteristic curves, and operating regions.
+    * Switching times as a bridge to transistor applications.
+    * FET and MOSFET operating principle.
+    * MOSFET channel formation, body diode, and MOSFET types.
+    * BJT versus MOSFET as switching element.
+  * **Practice (20 min):**
+    * Calculate collector current from base current and current gain.
+    * Decide whether a BJT is likely in cutoff, active region, or saturation.
+    * Estimate MOSFET conduction losses with \(R_{\rm DS(on)}\).
+    * Compare BJT and MOSFET control losses.
+  * **Wrap-up (5 min):**
+    * Summary: BJT is current-controlled in the simple model; MOSFET is voltage-controlled in the simple model.
+    * Preview: transistor applications such as low-side switches, high-side switches, PWM, relay drivers, and H-bridges are continued in [[block14|Block 14]].
+===== Conceptual overview =====
+<callout icon="fa fa-lightbulb-o" color="blue">
+  * A transistor is a semiconductor component where a **small control signal** influences a **larger load current**.
+  * A BJT uses a base current \(I_{\rm B}\) to control the collector current \(I_{\rm C}\).
+  * A MOSFET uses a gate-source voltage \(U_{\rm GS}\) to control the drain current \(I_{\rm D}\).
+  * BJTs and MOSFETs are both used as switches and amplifiers, but their control principles are different.
+  * A transistor does not create energy. The load energy comes from the supply. The transistor only controls how much current may flow.
+  * This block explains the component behavior. Circuit dimensioning and applications are treated in [[block14|Block 14]].
+</callout>
+~~PAGEBREAK~~ ~~CLEARFIX~~
+===== Core content =====
+<WRAP>
+<callout type="info" icon="true">
+==== Introductory example====
+The electronics in personal computers, mobile phones, electric toothbrushes, and like all other digital companions, are based on transistor circuits. All logic circuits can be traced back to NAND and NOR gates as building blocks. These logic gates consist of transistors. In the simulation below, the structure of a NAND gate is shown in the current CMOS structure. CMOS here indicates the structure of the circuit and semiconductor structure: **C**omplementary **m**etal-**o**xide-**s**emiconductor - an oppositely complementary circuit of semiconductors of the metal-oxide-semiconductor structure.
+The complementary structure is shown by the fact that.
+  * from the digital output ($OUT2$) to ground two transistors of one kind are connected in series and
+  * from the digital output ($OUT2$) to the $5~\rm V$ supply, two transistors of a different type are connected in parallel.
+These two different kinds of MOS-transistors and further used kinds shall be explained in this chapter.
+<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgDOB0YwTFBGAzEgHANgKzoOywCxKZJgCc+8CIm1EmApgLQIIBQAZiEuqiArL3wJ0fAdT6QaYaLA5ceIWARBCRS-ColSZrAO4rhffBtV8cIsHoMiE564rC9LAWRX5etkcY+l4EWJJyRPACgoahmgiSUGCy+qYEEAl44KwA5vYkJoZIsBD5VtweYkWKypacEfy8KDZiNFHasYXcIKgQtXz8qfqd7fb9lvGG-aYsfqwASgNJhu7gC-h0C-mB+lViERFDiqi8EcG7Ti02xlytnj3nNnZjdpbTzN2w2CDMm69UlDCK0QFSUEwUze40UKXe+xSX1ovxo-xWgTyOBBz1ejH6Ly8IAAkgA5NhIlEhcEYlIaPGyQmJMoaPL7ZTk-GsKlLI4OfZ7TQU1iuanqRSs6n+NYC-zKUr8nZ8zlbTkuUVs6lZBb-Kx3LzzS6WQneMxefqXDQAeQAqgAVWQITBUZhnapvA1ifwLIGE5joCCg5i+LrwRkEsDI92es7eyhnRmUwNvdAae2MXKiQQgU1mtiuRixpMxuNnYVA-Toz1iTNxp2sABGfB9icw0aQQlSVcYeVIXHgma4jcsAA83twvG2W2gQDg27SNLiAIK4gAijAA4gBDAAu9AAOuuAHZLgDO693FYANkuAMYAawrAHse6w+6063xMB5oxOQNO54w0quN9uK3v6AAEwPK8twPTctwAYWcI0AGUeRBD0jA0YM+CQ-MrFQhBQ2w3MNB2W0426LDunlEiO2EYsnFhVgliQdsaTQ-xXg6JAAH0EDYsA2KEWI2MwLjIE47jYDYlAxNosB6MTUFKOQhYkE44SeIQPiBOkZTRMUiS6IY3CmL1BTROU3jRPUoSuLYrStMk6SQk+JDtkUUgOMs0z+MEzSrJcpBWCAA noborder}}
+</WRAP>
+</callout></WRAP>
+==== From diode to transistor ====
+A variable resistor can be developed from the diode. \\
+A diode has two terminals and one pn junction, as we have seen in [[Block11]]. It can conduct or block depending on the applied voltage. \\ Therefore, there is only one path on which the current is dependent on the voltage on this path
+With this controlled transition resistor ("__tran__sfer re__sistor__" or better transistor) this gets a bit more extreenally controlled:
+  - A transistor has at least three terminals.
+  - One terminal is used to control the current path between the other two terminals.
+<panel type="info" title="Analogy: controlled valve">
+Imagine a water valve.
+  * A small movement of the handle controls the main water flow.
+  * The handle does not supply the water energy.
+  * The pressure source supplies the water energy.
+For a transistor:
+  * the control signal is the handle,
+  * the load current is the main water flow,
+  * the supply voltage provides the energy.
+</panel>
+<callout>
+A transistor is not simply “a stronger diode”.  \\
+It is a controlled component: one electrical variable changes the current through another path.
+</callout>
+~~PAGEBREAK~~ ~~CLEARFIX~~
+==== Bipolar junction transistor: structure and terminals ====
+A bipolar junction transistor (BJT) has three doped regions and three terminals.
+  * **Emitter \(E\):** emits charge carriers (either holes or electrons) into the transistor.
+  * **Base \(B\):** thin control region.
+  * **Collector \(C\):** collects charge carriers.
+There are two basic BJT types:
+  * **npn transistor:** n-p-n layer sequence,
+  * **pnp transistor:** p-n-p layer sequence.
+<WRAP>
+<panel type="default">
+<imgcaption fig_bjt_structure|Layer structure and circuit symbols of npn and pnp bipolar junction transistors.></imgcaption>
+{{:circuit_design:bipolartransistor_npn_oder_pnp_struktur.svg?650}}
+</panel>
+</WRAP>
+Depending on the layer sequence (or "direction of the diodes"), PNP or NPN transistors result, represented by different circuit symbols with three terminals (see <imgref fig_bjt_structure>). In both transistor variants, charge carriers are emitted from the emitter terminal (E) toward the collector terminal (C) if a suitable current flows through the base terminal (B). In simplified terms, the negative charge carriers of the n-doped sides could represent a current through an NPN structure if negative charge carriers were also present in the P-doped layer. The current $I_\rm C$ flowing with it in the technical current direction is illustrated in the circuit symbol by the arrow direction at the emitter. In the NPN transistor, the current $I_\rm C$ flows from the collector to the emitter. Since positive charge carriers enable conductivity in the PNP transistor, the technical current direction here points from the emitter to the collector, and the arrow on the emitter points towards the collector. The direction of the arrow is similar to the direction of the diode or the PN junction.
+<callout>
+**Mnemonic for the emitter arrow**
+  * **npn:** arrow **n**ot **p**ointing i**n**.
+  * **pnp:** arrow **p**oints i**n**.
+The arrow indicates the technical current direction at the emitter in normal operation.
+</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">
+A BJT can be drawn as two pn junctions, but it is **not** simply two independent diodes.
+The base region is very thin.
+This is essential: it allows charge carriers injected from the emitter to reach the collector.
+</panel>
+==== Correct connection and normal operation of an npn transistor ====
+<panel type="info" title="Simulation: correct transistor wiring">
+Things to try:
+  * compare npn and pnp polarity,
+  * observe which base-emitter voltage is needed,
+  * check the current direction through the collector-emitter path.
+{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjA7CAMB00OgVnLJA2ALAJnQZjAA5DMjDJsR0xwQlo6BTAWjDACgBzEPbB7Yjz49omGDHZEavBmExiZ4AJyUGBbAPQx4CGnD07oBxBwBKQ2fIvgwq8fTriGcJOwAeQpSA2EepbwQgYkQgAMLu3oRe2HhqRgF4QeC+AELsAC6RvtiYasI5zrTM2LDodmAIIAAmjABmAIYArgA26ewATuDo-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 700,500 noborder}}
+</panel>
+For an npn transistor in normal active operation, the base-emitter junction is forward-biased and the collector-base junction is reverse-biased.
+\[
+\begin{align*}
+U_{\rm BE} &> 0,
+&
+U_{\rm CE} &> 0,
+&
+U_{\rm CB} &> 0.
+\end{align*}
+\]
+With the reference arrows commonly used in this course:
+\[
+\begin{align*}
+I_{\rm B}>0,
+\qquad
+I_{\rm C}>0,
+\qquad
+I_{\rm E}<0.
+\end{align*}
+\]
+Kirchhoff's current law gives
+\[
+\begin{align*}
+I_{\rm B}+I_{\rm C}+I_{\rm E}=0.
+\end{align*}
+\]
+Using current magnitudes:
+\[
+\begin{align*}
+|I_{\rm E}|=I_{\rm B}+I_{\rm C}.
+\end{align*}
+\]
+<tabcaption tab_bjt_signs|Sign conventions in normal operation>
+^ Type ^ Voltage signs ^ Current signs with the shown reference arrows ^
+| npn | \(U_{\rm BE}>0\), \(U_{\rm CE}>0\), \(U_{\rm CB}>0\) | \(I_{\rm B}>0\), \(I_{\rm C}>0\), \(I_{\rm E}<0\) |
+| pnp | \(U_{\rm BE}<0\), \(U_{\rm CE}<0\), \(U_{\rm CB}<0\) | \(I_{\rm B}<0\), \(I_{\rm C}<0\), \(I_{\rm E}>0\) |
+</tabcaption>
+==== 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.
+For a silicon transistor, noticeable base current often starts around
+\[
+\begin{align*}
+U_{\rm BE}\approx 0.6\ldots0.7~{\rm V}.
+\end{align*}
+\]
+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.
+Because both electrons and holes contribute to the physical operation, the component is called **bipolar**.
+</panel>
+<callout>
+For the following explanations, npn transistors are used as the main example.
+For pnp transistors, polarities and current directions are reversed.
+</callout>
+==== 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).
+<WRAP><imgcaption picJ|function of NPN bipolar junction transistor>
+{{elektronische_schaltungstechnik:jbt_funktionsweise.jpg?400}}
+</imgcaption></WRAP>
+\[
+\begin{align*}
+\boxed{
+I_{\rm C}\approx B I_{\rm B}
+}
+\end{align*}
+\]
+The factor \(B\) is the DC current gain:
+\[
+\begin{align*}
+B=\frac{I_{\rm C}}{I_{\rm B}}.
+\end{align*}
+\]
+For small changes around an operating point, the small-signal current gain is
+\[
+\begin{align*}
+h_{\rm FE} = \beta
+=
+\frac{\Delta I_{\rm C}}{\Delta I_{\rm B}}
+=
+\frac{i_{\rm C}}{i_{\rm B}}
+\approx B.
+\end{align*}
+\]
+<panel type="info" title="Color scheme for the BJT control idea">
+\[
+\begin{align*}
+{\color{blue}{I_{\rm B}}}
+&:\text{ small control current},
+\\
+{\color{green}{I_{\rm C}}}
+&:\text{ larger controlled current},
+\\
+{\color{red}{U_{\rm BE}I_{\rm B}}}
+&:\text{ input control power}.
+\end{align*}
+\]
+The useful first approximation is
+\[
+\begin{align*}
+{\color{green}{I_{\rm C}}}
+\approx
+B\,{\color{blue}{I_{\rm B}}}.
+\end{align*}
+\]
+</panel>
+<callout type="warning" icon="true">
+The current gain \(B\) is not a precise constant.
+It depends on transistor type, temperature, collector current, and manufacturing variation.
+For robust switch design, one usually does **not** rely on the typical value of \(B\).
+This is treated in [[block14|Block 14]].
+</callout>
+==== BJT characteristic curves and differential quantities ====
+A transistor is nonlinear. Therefore we describe it by characteristic curves.
+Important BJT characteristics are:
+  * **Input characteristic:** \(I_{\rm B}(U_{\rm BE})\)  \\     The base-emitter path behaves approximately like a diode.
+  * **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
+\[
+\begin{align*}
+r_{\rm BE}
+&=
+\frac{\Delta U_{\rm BE}}{\Delta I_{\rm B}}
+=
+\frac{u_{\rm BE}}{i_{\rm B}},
+\\[4pt]
+r_{\rm CE}
+&=
+\frac{\Delta U_{\rm CE}}{\Delta I_{\rm C}}
+=
+\frac{u_{\rm CE}}{i_{\rm C}}.
+\end{align*}
+\]
+~~PAGEBREAK~~ ~~CLEARFIX~~
+==== BJT operating 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 ^
+| 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  |
+| saturation     | \(I_{\rm B}\) large enough, \\ \(U_{\rm CE}\) small  | transistor conducts strongly                  | closed switch     |
+</tabcaption>
+\\
+=== Switching view ===
+For a BJT used as a switch:
+  * **off:** cutoff region,
+  * **on:** saturation region.
+In saturation, the collector-emitter voltage is small, often approximated by
+\[
+\begin{align*}
+U_{\rm CE,sat}\approx 0.1\ldots 0.3~{\rm V}.
+\end{align*}
+\]
+The conduction loss of a saturated BJT switch is approximately
+\[
+\begin{align*}
+P_{\rm on,BJT}
+\approx
+U_{\rm CE,sat}I_{\rm C}.
+\end{align*}
+\]
+The control loss at the base is approximately
+\[
+\begin{align*}
+P_{\rm ctrl,BJT}
+\approx
+U_{\rm BE}I_{\rm B}.
+\end{align*}
+\]
+<callout>
+Detailed switch dimensioning, base resistor calculation, and switching inductive loads are continued in [[block14|Block 14]].
+</callout>
+=== Switching times of a BJT ===
+Real transistor switching is not instantaneous.
+{{drawio>electrical_engineering_and_electronics_2:switchingdiagram_v01.svg}}
+Typical time intervals are:
+<tabcaption tab_bjt_switching_times|BJT switching times>
+^ Symbol           ^ Meaning  ^
+| \(t_{\rm d}\)    | delay time           |
+| \(t_{\rm r}\)    | rise time            |
+| \(t_{\rm on}\)   | total turn-on time   |
+| \(t_{\rm s}\)    | storage time         |
+| \(t_{\rm f}\)    | fall time            |
+| \(t_{\rm off}\)  | total turn-off time  |
+</tabcaption>
+\\
+During switching, both current and voltage can be significant at the same time.  \\
+Therefore switching losses occur during turn-on and turn-off.
+\[
+\begin{align*}
+p(t)=u_{\rm CE}(t) \cdot i_{\rm C}(t).
+\end{align*}
+\]
+<panel type="info" title="Engineering interpretation">
+A BJT in saturation stores charge carriers in the base region.
+When switching off, this stored charge must be removed first.
+This contributes to the storage time \(t_{\rm s}\).
+</panel>
+~~PAGEBREAK~~ ~~CLEARFIX~~
+==== Field-effect transistor: basic idea ====
+A field-effect transistor controls current by an electric field.
+For a MOSFET:
+  * **gate \(G\):** control terminal,
+  * **source \(S\):** reference terminal for \(U_{\rm GS}\),
+  * **drain \(D\):** load current terminal,
+  * **bulk \(B\):** semiconductor body, often internally connected to source in discrete MOSFETs.
+The name MOSFET means:
+\[
+\begin{align*}
+\text{Metal-Oxide-Semiconductor Field-Effect Transistor}.
+\end{align*}
+\]
+<panel type="info" title="Key difference to the BJT">
+For a BJT:
+\[
+\begin{align*}
+{\color{blue}{I_{\rm B}}}
+\quad \text{controls} \quad
+{\color{green}{I_{\rm C}}}.
+\end{align*}
+\]
+For a MOSFET:
+\[
+\begin{align*}
+{\color{blue}{U_{\rm GS}}}
+\quad \text{controls} \quad
+{\color{green}{I_{\rm D}}}.
+\end{align*}
+\]
+In stationary operation, the ideal gate current is approximately
+\[
+\begin{align*}
+I_{\rm G}\approx 0.
+\end{align*}
+\]
+</panel>
+<WRAP>
+<panel type="default">
+<imgcaption fig_fet_principle|FET principle: a gate signal controls the drain-source current path.></imgcaption>
+{{:circuit_design:fet_prinzip.svg?650}}
+</panel>
+</WRAP>
+==== MOSFET structure and channel formation ====
+The gate is separated from the semiconductor by a thin oxide layer.
+Therefore the gate behaves approximately like one plate of a capacitor.
+<WRAP>
+<panel type="default">
+<imgcaption fig_mosfet_layering|Simplified layer structure of an n-channel enhancement MOSFET.></imgcaption>
+{{:circuit_design:mosfet_pinch_off.svg?650}}
+</panel>
+</WRAP>
+For an n-channel enhancement MOSFET:
+  * at \(U_{\rm GS}=0\), no conductive channel exists,
+  * when \(U_{\rm GS}\) becomes large enough, electrons form a channel,
+  * then drain current \(I_{\rm D}\) can flow.
+The threshold voltage \(U_{\rm GS(th)}\) indicates when a small channel just begins to form.
+<WRAP column 100%>
+<panel type="danger" title="Important datasheet warning">
+\(U_{\rm GS(th)}\) is **not** the voltage for a fully switched-on MOSFET.
+For low conduction loss, use the gate voltage at which the datasheet specifies $R_{\rm DS(on)}$.
+</panel>
+</WRAP>
+==== Body diode of a MOSFET ====
+In a discrete power MOSFET, the bulk is often internally connected to the source.
+Together with the drain region, this creates an internal pn junction. This is the **body diode**.
+<callout>
+A real MOSFET is therefore not an ideal bidirectional switch.
+The body diode may conduct when the drain-source voltage has the reverse polarity.
+</callout>
+<panel type="info" title="Simulation: MOSFET channel and body diode">
+Things to try:
+  * increase \(U_{\rm GS}\) and observe channel formation,
+  * reverse the drain-source polarity,
+  * observe when the body diode conducts.
+{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjA7CAMB00LDWkwA40DYCcAmArGrmtgMzGYj67hXRUCmAtGGAFADuITm+lu0NN178+MNgA9uhACwhcvaZjkKhcmfUDJhJOGl88zEh7RsB9eCEBxAMo6eMqAX1N8ER4RBz0IAKoAdAGdA4KCggEdoADVOJXpcCBoXTDiMcXQjPnowYljwCEp6UgRkBAR9OCQ4Usr4RBikuNw5BvkE8SkeUi80UmFcGnRKbpAAJXqRECLmzMnoOWg2ADdhMSmV0QKYT3od5FcC2Hx6mbWW4iEFgCd1+UFpPFuL8FK2Ee4IanBk98-sp-o0FldjtDmwAOa5U4nARbBZcFqQSgIh4LDqYfrgB7GIRgbD6YaWOzouSkTC9Fx4yaYIbyOQACjAAEo7DJyFTyRpeqSaU0QHTcMyOk1CmTuLihNzPLS+aQAIbMgRQBE5FrYGmRAAiGrYivepMxiQg+v65k12usesouMN+rA312ADNZQAbAIMLa4V7vGF2+hMBJZHK7QFi4F7Oz4Mi3DIQUwCczeQkdfD4OKkcn4UhCXD64a2ZOp25+zPZ6C9Ybajp6Ut+rr8MtS7yV7jV+Tplsyfi5iwgfPcDRIARGLOOOaNqwsooG-t2zH4nuE+GknH5FuYHEo8FriVjpjLyYwnZsa5MTsqO6n4oCJ5gF5L9ezZr787iZan5SP-sfgibegaeSwocq5wEc8Jnp+e4PmsqL9jIAw9P2U6DOOoz1M+vKQdmbQLOk27gCq+6Ils2TYPMtRlMgNTVCUdT3lhiTPqkMGnim8isXuaD6AQag9v4oQhMEYS4NEHQyKyBhGDIkBmChNh2COBjOKSjgPuoWj1OB15fioYjMXa9Z+mA+DnuWPbNiw1JtuSRkqN23h9kwAhxtARi4lxY4EnYOYbokJpzrJ9REURLCrta4gQiFlCnER5DAse3DxDQWmOXcWlAgggWrtFq4vgsb6JRBBU-rC2xUIB+zhvCBXZVFY7MQQWQIY5WYWDS3hjPCRF+ZFrQ0DhaCuaFKpBcBVKcbGNEURUk1UbRYo5W0PW5V5opOGKUbcShfECfxYT4CJCX4IOhgJQQMkEg5uIqc0kAqVAakgNoVVtMlRW6TEbJ+bOflwge06zmFCwACZ-X5bJhTQQMME6ACuzoAC71CGyXI+9yYyUZBj3aV2jJnGJ17r0CgJlYDkQIO7EUzx3jbfxu37TE31tN9TFsLhAM5ADo3Lq4phVKU5QoDNM2M-wvJM31EY4k1natShHXcCGayztBSyK4Uu6o7+pXlHswGglwKtjizFzxUwyMXt9dzpQsEJG14UWHuIhtWqFVqbqJ7sMQMlKeR00lDi2twkyASb9hKoo8FSPL0qQABGzIOvcSUXjMWng4cJSeknl5xBez53BngvQNnCWpZbOWFwMmdVKXFmPF8DdF1nOrQEqhEEQ+apSmardKkFw2rt3ci97qHM4pQw8gL3QA 700,500 noborder}}
+</panel>
+~~PAGEBREAK~~ ~~CLEARFIX~~
+==== MOSFET output characteristics ====
+The drain current $I_{\rm D}$ depends on
+  * the drain-source voltage $U_{\rm DS}$, and
+  * the gate-source voltage $U_{\rm GS}$.
+{{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}}
+\\
+<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     ^
+| 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   |
+| 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.
+  * BJT saturation: good for a closed switch.
+  * MOSFET saturation: not the usual low-loss switch region.
+A fully switched-on MOSFET is usually operated in the linear or ohmic region.
+</callout>
+When a MOSFET is fully switched on, the drain-source path behaves approximately like a small resistance:
+\[
+\begin{align*}
+U_{\rm DS}\approx R_{\rm DS(on)} \cdot I_{\rm D}.
+\end{align*}
+\]
+The conduction loss is
+\[
+\begin{align*}
+\boxed{
+P_{\rm on,MOS}
+=
+R_{\rm DS(on)} \cdot I_{\rm D}^2
+}
+\end{align*}
+\]
+==== MOSFET types ====
+MOSFETs can be classified by channel type and by whether they are normally off or normally on.
+<WRAP>
+<panel type="default">
+<imgcaption fig_mosfet_symbols|Circuit symbols for common MOSFET types.></imgcaption>
+{{:circuit_design:fet_schaltsymbol.svg?650}}
+</panel>
+</WRAP>
+<tabcaption tab_mosfet_types|Basic MOSFET types>
+^ 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 \(U_{\rm GS}\)  |
+| 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**.
+==== BJT versus MOSFET as a switch ====
+<tabcaption tab_bjt_mosfet_comparison|BJT and MOSFET as switching elements>
+^ Property                    ^ BJT  ^ MOSFET  ^
+| control quantity            | base current \(I_{\rm B}\)                     | gate-source voltage \(U_{\rm GS}\)                                    |
+| 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  |
+| 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                            |
+| 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. \\
+</callout>
+<panel type="info" title="Engineering preview">
+In many modern digital and power-electronic circuits, MOSFETs are preferred as switches because they need almost no stationary gate current and can have very small \(R_{\rm DS(on)}\).
+However, the gate is capacitive.
+Fast switching requires charging and discharging this capacitance quickly.
+This is one reason why gate drivers are needed in power stages.
+</panel>
+~~PAGEBREAK~~ ~~CLEARFIX~~
+===== Exercises =====
+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee2_taskctr#~~.1 BJT terminals, signs, and current balance
+#@TaskText_HTML@#
+An npn transistor is operated in normal active operation.
+The reference arrows are chosen as in the core content:
+  * \(I_{\rm B}\) and \(I_{\rm C}\) enter the transistor,
+  * \(I_{\rm E}\) is also defined as entering the transistor.
+For normal npn operation:
+\[
+\begin{align*}
+U_{\rm BE}>0,
+\qquad
+U_{\rm CE}>0,
+\qquad
+U_{\rm CB}>0.
+\end{align*}
+\]
+. State the meaning of the terminals \(B\), \(C\), and \(E\).
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13001~@#
+<WRAP leftalign>
+Use the terminal names of the bipolar junction transistor:
+  * \(B\): control terminal,
+  * \(C\): terminal of the main current path,
+  * \(E\): terminal where carriers are emitted.
+The names are not arbitrary. They describe the physical function of the regions.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13001~@#
+\[
+\begin{align*}
+B&:\text{ base},\\
+C&:\text{ collector},\\
+E&:\text{ emitter}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. State the signs of \(I_{\rm B}\), \(I_{\rm C}\), and \(I_{\rm E}\) in normal npn operation.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13002~@#
+<WRAP leftalign>
+For the reference arrows used here, base current and collector current enter the transistor.
+The emitter current physically leaves the transistor.
+Since \(I_{\rm E}\) is also defined as entering the transistor, its sign becomes negative.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13002~@#
+\[
+\begin{align*}
+I_{\rm B}>0,
+\qquad
+I_{\rm C}>0,
+\qquad
+I_{\rm E}<0.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate \(I_{\rm E}\) for
+\[
+\begin{align*}
+I_{\rm B}=50~\mu{\rm A},
+\qquad
+I_{\rm C}=5.0~{\rm mA}.
+\end{align*}
+\]
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13003~@#
+<WRAP leftalign>
+Apply Kirchhoff's current law at the transistor:
+\[
+\begin{align*}
+I_{\rm B}+I_{\rm C}+I_{\rm E}=0.
+\end{align*}
+\]
+Solve for \(I_{\rm E}\):
+\[
+\begin{align*}
+I_{\rm E}=-(I_{\rm B}+I_{\rm C}).
+\end{align*}
+\]
+Insert both currents in the same unit:
+\[
+\begin{align*}
+I_{\rm B}=50~\mu{\rm A}=0.050~{\rm mA}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13003~@#
+\[
+\begin{align*}
+I_{\rm E}
+&=
+-\left(0.050~{\rm mA}+5.0~{\rm mA}\right)
+\\
+&=
+-5.05~{\rm mA}.
+\end{align*}
+\]
+The emitter current magnitude is
+\[
+\begin{align*}
+|I_{\rm E}|=5.05~{\rm mA}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+#@TaskEnd_HTML@#
+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee2_taskctr#~~.1 BJT current gain and active-region estimate
+#@TaskText_HTML@#
+An npn transistor is operated in the active region.
+The base current is
+\[
+\begin{align*}
+I_{\rm B}=35~\mu{\rm A}.
+\end{align*}
+\]
+The DC current gain is approximated by
+\[
+\begin{align*}
+B=150.
+\end{align*}
+\]
+. Calculate the collector current \(I_{\rm C}\).
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13004~@#
+<WRAP leftalign>
+In the active region, use the current-gain approximation
+\[
+\begin{align*}
+I_{\rm C}\approx B I_{\rm B}.
+\end{align*}
+\]
+Insert the given current gain and base current.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13004~@#
+\[
+\begin{align*}
+I_{\rm C}
+&\approx
+B I_{\rm B}
+\\
+&=
+\cdot 35~\mu{\rm A}
+\\
+&=
+~\mu{\rm A}
+=
+.25~{\rm mA}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate the emitter current magnitude \(|I_{\rm E}|\).
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13005~@#
+<WRAP leftalign>
+Using magnitudes,
+\[
+\begin{align*}
+|I_{\rm E}|=I_{\rm B}+I_{\rm C}.
+\end{align*}
+\]
+Convert \(I_{\rm B}\) to \({\rm mA}\):
+\[
+\begin{align*}
+~\mu{\rm A}=0.035~{\rm mA}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13005~@#
+\[
+\begin{align*}
+|I_{\rm E}|
+&=
+.035~{\rm mA}+5.25~{\rm mA}
+\\
+&=
+.285~{\rm mA}
+\approx
+.29~{\rm mA}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Explain why the value of \(I_{\rm C}\) is only an estimate.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13006~@#
+<WRAP leftalign>
+The formula
+\[
+\begin{align*}
+I_{\rm C}\approx B I_{\rm B}
+\end{align*}
+\]
+uses a simplified transistor model.
+The current gain \(B\) is not an exact constant.
+It depends on transistor type, collector current, temperature, and manufacturing variation.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13006~@#
+The collector current is only an estimate because \(B\) can vary strongly.
+For robust circuit design, especially for switches, one should not rely only on a typical value of \(B\).
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+#@TaskEnd_HTML@#
+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee2_taskctr#~~.1 Cutoff, active region, or saturation?
+#@TaskText_HTML@#
+An npn transistor is used with a resistive load.
+The supply voltage is
+\[
+\begin{align*}
+U_{\rm dc}=12~{\rm V}.
+\end{align*}
+\]
+The load resistance is
+\[
+\begin{align*}
+R_{\rm L}=680~\Omega.
+\end{align*}
+\]
+The base current is
+\[
+\begin{align*}
+I_{\rm B}=0.15~{\rm mA}.
+\end{align*}
+\]
+Assume a current gain
+\[
+\begin{align*}
+B=100.
+\end{align*}
+\]
+. Calculate the collector current predicted by the active-region formula.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13007~@#
+<WRAP leftalign>
+If the transistor is in the active region, use
+\[
+\begin{align*}
+I_{\rm C,active}\approx B I_{\rm B}.
+\end{align*}
+\]
+This is the collector current the transistor would try to set.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13007~@#
+\[
+\begin{align*}
+I_{\rm C,active}
+&\approx
+\cdot 0.15~{\rm mA}
+\\
+&=
+~{\rm mA}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate the maximum load current set by the resistor.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13008~@#
+<WRAP leftalign>
+The load circuit limits the current.
+As a first estimate, neglect \(U_{\rm CE,sat}\) and use Ohm's law:
+\[
+\begin{align*}
+I_{\rm L,max}\approx \frac{U_{\rm dc}}{R_{\rm L}}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13008~@#
+\[
+\begin{align*}
+I_{\rm L,max}
+&\approx
+\frac{12~{\rm V}}{680~\Omega}
+\\
+&=
+.6~{\rm mA}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Decide whether the transistor is likely in the active region or in saturation.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13009~@#
+<WRAP leftalign>
+Compare the current predicted by the active-region formula with the maximum current allowed by the load circuit:
+\[
+\begin{align*}
+I_{\rm C,active}
+\quad \text{versus} \quad
+I_{\rm L,max}.
+\end{align*}
+\]
+If \(I_{\rm C,active}\) is smaller than the load limit, the transistor can still be in the active region.
+If \(I_{\rm C,active}\) is larger than the load limit, the transistor is driven into saturation.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13009~@#
+\[
+\begin{align*}
+I_{\rm C,active}=15~{\rm mA}
+<
+I_{\rm L,max}=17.6~{\rm mA}.
+\end{align*}
+\]
+The transistor is not forced into saturation by this base current.
+It is likely still in the active region.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. What base current would approximately be required to reach the load-current limit in the active-region model?
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13010~@#
+<WRAP leftalign>
+Set the active-region collector current equal to the maximum load current:
+\[
+\begin{align*}
+I_{\rm L,max}=B I_{\rm B,limit}.
+\end{align*}
+\]
+Solve for the base current:
+\[
+\begin{align*}
+I_{\rm B,limit}=\frac{I_{\rm L,max}}{B}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13010~@#
+\[
+\begin{align*}
+I_{\rm B,limit}
+&=
+\frac{17.6~{\rm mA}}{100}
+\\
+&=
+.176~{\rm mA}.
+\end{align*}
+\]
+So a base current above about
+\[
+\begin{align*}
+I_{\rm B}\approx 0.18~{\rm mA}
+\end{align*}
+\]
+would begin to drive the transistor toward saturation.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+#@TaskEnd_HTML@#
+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee2_taskctr#~~.1 MOSFET threshold voltage versus fully switched-on operation
+#@TaskText_HTML@#
+An n-channel enhancement MOSFET is used as a switch.
+The datasheet gives
+\[
+\begin{align*}
+U_{\rm GS(th)}=2.0\ldots4.0~{\rm V}.
+\end{align*}
+\]
+The datasheet also gives
+\[
+\begin{align*}
+R_{\rm DS(on)}=80~{\rm m}\Omega
+\end{align*}
+\]
+but only for
+\[
+\begin{align*}
+U_{\rm GS}=10~{\rm V}.
+\end{align*}
+\]
+The load current is
+\[
+\begin{align*}
+I_{\rm D}=3.0~{\rm A}.
+\end{align*}
+\]
+. Explain why \(U_{\rm GS(th)}\) is not the correct value for switching the MOSFET fully on.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13011~@#
+<WRAP leftalign>
+The threshold voltage only describes the beginning of channel formation.
+At \(U_{\rm GS(th)}\), the datasheet usually defines only a very small drain current.
+For low-loss switching, the MOSFET must have a small \(R_{\rm DS(on)}\).
+Therefore use the gate voltage for which \(R_{\rm DS(on)}\) is specified.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13011~@#
+\(U_{\rm GS(th)}\) means: the MOSFET just starts to conduct.
+It does **not** mean: the MOSFET is a good low-resistance switch.
+For this datasheet value, low-loss operation is specified at
+\[
+\begin{align*}
+U_{\rm GS}=10~{\rm V}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate the drain-source voltage \(U_{\rm DS}\) when the MOSFET is fully switched on at \(U_{\rm GS}=10~{\rm V}\).
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13012~@#
+<WRAP leftalign>
+For a fully switched-on MOSFET, use the resistor approximation:
+\[
+\begin{align*}
+U_{\rm DS}\approx R_{\rm DS(on)}I_{\rm D}.
+\end{align*}
+\]
+Convert the resistance:
+\[
+\begin{align*}
+~{\rm m}\Omega=0.080~\Omega.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13012~@#
+\[
+\begin{align*}
+U_{\rm DS}
+&\approx
+.080~\Omega\cdot 3.0~{\rm A}
+\\
+&=
+.24~{\rm V}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate the conduction loss \(P_{\rm on,MOS}\).
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13013~@#
+<WRAP leftalign>
+The conduction loss of a switched-on MOSFET is
+\[
+\begin{align*}
+P_{\rm on,MOS}=R_{\rm DS(on)}I_{\rm D}^2.
+\end{align*}
+\]
+Alternatively, you can use
+\[
+\begin{align*}
+P_{\rm on,MOS}=U_{\rm DS}I_{\rm D}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13013~@#
+\[
+\begin{align*}
+P_{\rm on,MOS}
+&=
+.080~\Omega\cdot (3.0~{\rm A})^2
+\\
+&=
+.080~\Omega\cdot 9.0~{\rm A^2}
+\\
+&=
+.72~{\rm W}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+#@TaskEnd_HTML@#
+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee2_taskctr#~~.1 BJT versus MOSFET as a switching element
+#@TaskText_HTML@#
+A mechatronic actuator draws the load current
+\[
+\begin{align*}
+I_{\rm L}=1.2~{\rm A}.
+\end{align*}
+\]
+Two possible switching transistors are compared.
+For the BJT, assume
+\[
+\begin{align*}
+U_{\rm CE,sat}=0.25~{\rm V},
+\qquad
+U_{\rm BE}=0.70~{\rm V},
+\qquad
+I_{\rm B}=15~{\rm mA}.
+\end{align*}
+\]
+For the MOSFET, assume
+\[
+\begin{align*}
+R_{\rm DS(on)}=120~{\rm m}\Omega
+\end{align*}
+\]
+at the available gate voltage.
+. Calculate the BJT conduction loss.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13014~@#
+<WRAP leftalign>
+For a saturated BJT switch, the conduction loss is approximated by
+\[
+\begin{align*}
+P_{\rm on,BJT}\approx U_{\rm CE,sat}I_{\rm C}.
+\end{align*}
+\]
+Here the collector current is the load current:
+\[
+\begin{align*}
+I_{\rm C}\approx I_{\rm L}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13014~@#
+\[
+\begin{align*}
+P_{\rm on,BJT}
+&\approx
+.25~{\rm V}\cdot 1.2~{\rm A}
+\\
+&=
+.30~{\rm W}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate the stationary BJT control loss at the base.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13015~@#
+<WRAP leftalign>
+The base-emitter path behaves approximately like a forward-biased diode.
+The stationary control loss is
+\[
+\begin{align*}
+P_{\rm ctrl,BJT}\approx U_{\rm BE}I_{\rm B}.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13015~@#
+\[
+\begin{align*}
+P_{\rm ctrl,BJT}
+&\approx
+.70~{\rm V}\cdot 15~{\rm mA}
+\\
+&=
+.5~{\rm mW}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Calculate the MOSFET conduction loss.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13016~@#
+<WRAP leftalign>
+For a fully switched-on MOSFET, use
+\[
+\begin{align*}
+P_{\rm on,MOS}=R_{\rm DS(on)}I_{\rm D}^2.
+\end{align*}
+\]
+Here the drain current is the load current:
+\[
+\begin{align*}
+I_{\rm D}\approx I_{\rm L}.
+\end{align*}
+\]
+Convert
+\[
+\begin{align*}
+~{\rm m}\Omega=0.120~\Omega.
+\end{align*}
+\]
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13016~@#
+\[
+\begin{align*}
+P_{\rm on,MOS}
+&=
+.120~\Omega\cdot (1.2~{\rm A})^2
+\\
+&=
+.120~\Omega\cdot 1.44~{\rm A^2}
+\\
+&=
+.173~{\rm W}.
+\end{align*}
+\]
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Which component has the lower on-state loss in this operating point?
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13017~@#
+<WRAP leftalign>
+Compare the calculated conduction losses:
+\[
+\begin{align*}
+P_{\rm on,BJT}
+\quad \text{and} \quad
+P_{\rm on,MOS}.
+\end{align*}
+\]
+The lower value means lower heat generation in the switched-on state.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13017~@#
+\[
+\begin{align*}
+P_{\rm on,MOS}=0.173~{\rm W}
+<
+P_{\rm on,BJT}=0.30~{\rm W}.
+\end{align*}
+\]
+For this operating point, the MOSFET has the lower conduction loss.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. State one important disadvantage or risk of each device.
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13018~@#
+<WRAP leftalign>
+Use the qualitative comparison:
+  * BJT: controlled by base current.
+  * MOSFET: controlled by gate-source voltage.
+  * BJT switching can be affected by current gain and stored charge.
+  * MOSFET switching can be affected by gate oxide limits and gate charge.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13018~@#
+Possible answer:
+  * **BJT:** needs continuous base current; current gain \(B\) varies strongly.
+  * **MOSFET:** gate oxide is sensitive to overvoltage and ESD; the gate capacitance must be charged and discharged during switching.
+Both devices must be checked for power dissipation and temperature.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+#@TaskEnd_HTML@#
+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee2_taskctr#~~.1 MOSFET body diode and current direction
+#@TaskText_HTML@#
+A discrete n-channel MOSFET is used as a low-side switch.
+The source is connected to ground, the drain is connected to a load, and the load is connected to \(+24~{\rm V}\).
+The MOSFET is off:
+\[
+\begin{align*}
+U_{\rm GS}=0.
+\end{align*}
+\]
+. Can the MOSFET channel conduct a useful load current?
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13019~@#
+<WRAP leftalign>
+For an n-channel enhancement MOSFET:
+  * at \(U_{\rm GS}=0\), no useful channel exists,
+  * a positive gate-source voltage is required to form the channel.
+Therefore the drain-source path through the channel is off.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13019~@#
+No.
+At
+\[
+\begin{align*}
+U_{\rm GS}=0
+\end{align*}
+\]
+an n-channel enhancement MOSFET is normally off, so the channel does not conduct a useful load current.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Why is a real MOSFET still not an ideal bidirectional open switch?
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13020~@#
+<WRAP leftalign>
+A discrete power MOSFET usually contains a body diode.
+This diode is caused by the internal pn junction between body and drain/source regions.
+Even when the MOSFET channel is off, the body diode can conduct for one drain-source polarity.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13020~@#
+A real MOSFET contains a body diode.
+Therefore it can block well only in one polarity.
+In the opposite polarity, the body diode may become forward-biased and conduct.
+So a single MOSFET is not an ideal bidirectional open switch.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+. Why is the body diode important for motor-driver circuits?
+<WRAP group>
+<WRAP half column rightalign>
+#@PathBegin_HTML~13021~@#
+<WRAP leftalign>
+Motors and coils are inductive loads.
+Their current cannot change instantly.
+When a transistor switches off, the current may continue through diodes or body diodes.
+This influences voltage spikes, current paths, losses, and braking behavior.
+</WRAP>
+#@PathEnd_HTML@#
+</WRAP>
+<WRAP half column>
+#@ResultBegin_HTML~13021~@#
+The body diode can provide a current path for inductive current.
+This can be useful, but it also affects the behavior of H-bridges and motor drivers.
+The designer must know when the body diode conducts and whether its current and power limits are sufficient.
+#@ResultEnd_HTML@#
+</WRAP>
+</WRAP>
+#@TaskEnd_HTML@#
+===== Common pitfalls =====
+  * **Thinking a BJT is just two diodes:** The thin base region makes transistor action possible. Two separate diodes do not behave like a transistor.
+  * **Forgetting the base-emitter diode:** The BJT input characteristic resembles a diode. For silicon, \(U_{\rm BE}\) is often around \(0.6\ldots0.7~{\rm V}\), depending on current and temperature.
+  * **Treating \(B\) as an exact constant:** The current gain can vary strongly. Robust switching circuits are not designed with a typical \(B\) only.
+  * **Confusing active region and saturation:** In the active region, \(I_{\rm C}\approx B I_{\rm B}\). In saturation, the load circuit limits \(I_{\rm C}\).
+  * **Using MOSFET threshold voltage as full-on voltage:** \(U_{\rm GS(th)}\) is not sufficient for low conduction loss.
+  * **Confusing MOSFET saturation with BJT saturation:** A fully switched-on MOSFET is usually in the linear or ohmic region, not in the MOSFET saturation region.
+  * **Forgetting the MOSFET body diode:** A real power MOSFET is not an ideal bidirectional switch.
+  * **Ignoring MOSFET gate charge:** The stationary gate current is nearly zero, but fast switching still requires charging and discharging the gate capacitance.
+  * **Mixing voltage polarities for pnp and p-channel devices:** Their useful operating polarities are reversed compared with npn and n-channel devices.
+  * **Ignoring power dissipation:** Both BJTs and MOSFETs convert electrical energy into heat during conduction and switching.
+===== Embedded resources =====
+<WRAP>
+{{youtube>Xli6HK2dkvQ}} \\
+Functional Principle of a Transistor
+</WRAP>
+~~PAGEBREAK~~ ~~CLEARFIX~~