After this chapter you will know all the basics around semiconductor components like diodes, transistors (BJT as well as MOSFETs) and their effects...
Electronics 103 – nonlinear components
After our first look into electronics, we now want to deepen our understanding of components such as diodes and – even more importantly – transistors and CMOS technology. We want to show that a transistor can behave both as an analog and as a digital device, depending only on the level – or layer of abstraction – from which you observe it.
Semiconductor materials
Let us start our tour of semiconductor devices with a short repetition of this topic from electronics 101.
If we make sure that the semiconductor material, here silicon, is not contaminated or doped with any trivalent or pentavalent atoms, the only relevant factor is temperature. At room temperature (≈ 25 °C), intrinsic silicon is a very poor conductor.
n-type doping (pentavalent donors)
When silicon is doped with atoms that have five valence electrons (pentavalent donors), one extra electron remains weakly bound and can easily move into the conduction band. This creates n-type (negative) semiconductor material.
Examples of pentavalent donor elements (Group V): |
p-type doping (trivalent acceptors)
When silicon is doped with atoms that have three valence electrons (trivalent acceptors), one electron is missing in the lattice. This “hole” behaves like a positive mobile charge carrier and creates p-type (positive) semiconductor material.
Examples of trivalent acceptor elements (Group III): |
Combining p-type and n-type material
When we bring n-doped and p-doped semiconductor material together, a pn-junction forms. This junction shows very interesting and highly useful behaviour: a depletion zone is created, internal electric fields arise, and the device becomes direction-dependent. All modern diodes, transistors, and CMOS structures are based on this fundamental effect.
Applications of diodes
The diode as rectifier
The half wave rectifier
The simplest possible - but highly inefficient rectifier is the half wave rectifier we introduce here.
It is a simple diode put in the forward direction…

As diode we introducing here the 1N4148 which is a popular signal diode but untypical as a rectifer diode - As we can see only one half of the sine wave is used…
Below, there is the same circuit but with a capacitor to eliminate the ripples…

The full wave rectifier
To make the rectifer more efficient we also utilize the negative part of the sine wave to create our DC Voltage


The (simple) LED circuit
First we want to show one of the simplest possible circuits, some that lighten your day (or night, pun intended).
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A light emitting diode (LED) does not go without its pre-resistor which is there to limit the currents that goes thru the LED. You can take a resistor from 1kOhm to 10kOhm,the precise vale is in most csases uncritical… But for you to verify the equation is as follows:
\large \[ R_{V} = \frac{U_{\text{Total}} - U_{R}}{I} \]
With that equation we can calculate the value for the resistor - after calculation we just use the next-higher available resistor in the E24 series. In most cases you can simply choose 1kOm resistor that will do it, Also, for the purposes I describe here, 1/4 Watt resistor are sufficient, even 1/8 Watt resistors are.
Now, we want to see happens when we switch the poles, then the diode is working in reverse polarity and so not lighting up…
LEDs came in a big variety of different sizes, shapes and colors, for example size differs in different smd sizes e.g. 0805 as well as in different shapes (see here). But first and foremost color is crucial. The different dotation make up for different colors.


Bipolar transistors and their applications
When we extend the pn-junction used in diodes as shown in the section above now we get from simple to the the so called BJT (bipolar junction transistor). There are two different versions of BJTs (named after their dotations): The NPN transistor and the PNP transistor.
Case | Picture |
TO-92 |
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Type | Symbol | Structure |
BC-547 (TO-92) | ||
BC-557 (TO-92) |
The simple circuit
There are a gazillion of applications for either BJTs as switch as well as amplifier - in the following we only want to visit the most vital applications (of both types). For the following example it works as an amplifier. But we also use it for logic circuit as shown here.
The simple circuit with negative feedback
Imagine you bought a bag full of BC547 , the most popular npn Transistors. If you measure them out, you will notice that there is a wide distribution of their properties. If you decide some BC547 from different charges respectively different companies, you will notice an even wider distribution of their mein parameters.
Therefore, we introduce the systemic principle of a negative feedback loop.
Negative feedback
Another quite proper method ist to engage a negative feedback… If part of the output voltage is fed back to the input of an amplifier, this is called feedback. In-phase feedback is called “positive feedback”; in this case, the fed-back output signal is added to the input signal, leading to self-excitation (resonance). Opposite-phase feedback is called negative feedback; in this case, the returned output voltage cancels out part of the input voltage. In relation to the magnitude of the output signal, negative feedback therefore acts as a significant reduction in amplification (a reduced input signal leads to a correspondingly smaller output signal).
So why use negative feedback?
This negative feedback has one disadvantage but multiple great advantages over the normal circuit without the control loop. We make a lesser great amplification gain, but adopt a far better amplifier circuit - greater bandwidth, less distortion factor…
Values fo this feedback resistor should be 30 to 70kOhm…
BJT as Switch
The flipflop
Another vital application, we already visited some time ago, is the application as a flip-flop as shown here. The flipflop is a central component in almost all digital circuit, which stores digital values (0 and 1)
Symbol | logic Circuit | detailed circuit |
The astable multivibrator
The so-called astable multivibrator is, in layman’s terms, a blinker circuit. The formula to compute the oscillation frequency from the given parameters is:
\large \[ f = \frac{1}{T} = \frac{1}{(R_{B1} \cdot C_1 + R_{B2} \cdot C_2)\,\ln(2)} \]

The formula for the frequency ($f$) of an astable multivibrator, which is $f = \frac{1}{(R_{B1} \cdot C_1 + R_{B2} \cdot C_2)\,\ln(2)}$, is derived by analyzing the charging and discharging cycles of the capacitors ($C_1$ and $C_2$) through the base resistors ($R_{B1}$ and $R_{B2}$).
Here is the step-by-step derivation for the periodic time ($T$), from which the frequency ($f$) is easily found.
1. Astable Multivibrator Operation
An astable multivibrator consists of two cross-coupled common-emitter transistor stages ($Q_1$ and $Q_2$).
The circuit alternates between two quasi-stable states:
State 1: $Q_1$ is ON (saturated), and $Q_2$ is OFF (cut-off).
State 2: $Q_1$ is OFF, and $Q_2$ is ON.
The transition from one state to the other is controlled by the charging of the coupling capacitors ($C_1$ and $C_2$) through the base resistors ($R_{B1}$ and $R_{B2}$).
Let’s analyze the first half-cycle, $T_1$, when $Q_1$ is OFF and $Q_2$ is ON.
2. Derivation of the Half-Period $T_1$
Assume the transition just occurred, and $Q_2$ is ON (saturated, $V_{CE2} \approx 0 \text{ V}$) and $Q_1$ is OFF ($V_{CE1} \approx V_{CC}$).
Initial Condition of $C_1$
When $Q_1$ was just turned OFF, its collector voltage ($V_{C1}$) shot up to $V_{CC}$.
Since $C_2$ couples $V_{C1}$ to the base of $Q_2$ ($V_{B2}$), the sudden rise in $V_{C1}$ caused $V_{B2}$ to rise, turning $Q_2$ ON.
Simultaneously, when $Q_2$ was just turned ON, its collector voltage ($V_{C2}$) dropped to $\approx 0 \text{ V}$.
Since $C_1$ couples $V_{C2}$ to the base of $Q_1$ ($V_{B1}$), the sudden drop in $V_{C2}$ drives $V_{B1}$ to a negative voltage. Specifically, $V_{B1} \approx -V_{CC}$.
Charging of $C_1$
With $Q_1$ OFF, the capacitor $C_1$ starts to charge up from its initial voltage, $V_{B1}(0) \approx -V_{CC}$, towards the supply voltage $V_{CC}$ through the resistor $R_{B1}$ and the saturated $Q_2$ ($V_{CE2} \approx 0 \text{ V}$).
The general equation for a capacitor charging in an RC circuit is: V_C(t) = V_F - (V_F - V_I)e^{-t/\tau} Where:
$V_C(t)$ is the capacitor voltage (which is $V_{B1}$ in this case).
$V_F$ is the final (target) voltage = $V_{CC}$ (the voltage $C_1$ is charging towards).
$V_I$ is the initial voltage = $-V_{CC}$.
$\tau$ is the time constant = $R_{B1}C_1$.
Substituting these values: V_{B1}(t) = V_{CC} - (V_{CC} - (-V_{CC}))e^{-t/(R_{B1}C_1)} V_{B1}(t) = V_{CC} - 2V_{CC}e^{-t/(R_{B1}C_1)}
End of Half-Period $T_1$
The half-period $T_1$ ends when $Q_1$ turns ON again, which happens when its base-emitter junction becomes forward-biased, i.e., when $V_{B1}$ reaches the cut-in voltage ($V_{cut-in} \approx 0.7 \text{ V}$ for silicon, but often approximated as $0 \text{ V}$ for simplicity in the derivation).
Set $V_{B1}(t) = 0 \text{ V}$ and $t = T_1$: 0 = V_{CC} - 2V_{CC}e^{-T_1/(R_{B1}C_1)}
Rearrange the equation: 2V_{CC}e^{-T_1/(R_{B1}C_1)} = V_{CC} e^{-T_1/(R_{B1}C_1)} = \frac{V_{CC}}{2V_{CC}} = \frac{1}{2}
Take the natural logarithm ($\ln$) of both sides: -\frac{T_1}{R_{B1}C_1} = \ln\left(\frac{1}{2}\right) Using the logarithm rule $\ln(a/b) = -\ln(b/a)$: -\frac{T_1}{R_{B1}C_1} = -\ln(2)
Solve for $T_1$: T_1 = R_{B1}C_1 \cdot \ln(2)
3. Derivation of the Half-Period $T_2$
By a symmetrical analysis of the second half-cycle ($T_2$), where $Q_1$ is ON and $Q_2$ is OFF, the role of $R_{B1}C_1$ is taken over by $R_{B2}C_2$.
The time constant for the charging of $C_2$ through $R_{B2}$ is $\tau_2 = R_{B2}C_2$.
Following the exact same steps, we find: T_2 = R_{B2}C_2 \cdot \ln(2)
4. Final Formula for Frequency ($f$)
Periodic Time ($T$)
The total periodic time $T$ is the sum of the two half-periods: T = T_1 + T_2 T = (R_{B1}C_1 \cdot \ln(2)) + (R_{B2}C_2 \cdot \ln(2)) T = (R_{B1}C_1 + R_{B2}C_2) \cdot \ln(2)
Frequency ($f$)
The frequency is the reciprocal of the periodic time: f = \frac{1}{T} \bbox[#D3D3D3]{\mathbf{f = \frac{1}{(R_{B1}C_1 + R_{B2}C_2) \cdot \ln(2)}}}
Symmetrical Case
In the common case where $R_{B1} = R_{B2} = R$ and $C_1 = C_2 = C$: T = (RC + RC) \cdot \ln(2) = 2RC \cdot \ln(2) Since $\ln(2) \approx 0.693$: T \approx 1.386 RC And the frequency is: f = \frac{1}{T} = \frac{1}{2RC \cdot \ln(2)} \bbox[#D3D3D3]{\mathbf{f \approx \frac{0.72}{RC}}}
Would you like to see a comparison of astable, monostable, and bistable multivibrators?
BJT as Amplifier
This chapter I will mostly be written 1:1 from the book "Wege in die Elektonik" from Joseph Glagla and Gert Lindner; 1980.
Two-Port-Theory Basic circuits and h-parameters
The two-port-theory and the h-parameters are theoretical foundation for two-port-schematics. It is utilized for example to describe amplifiers, all circuits discussed here have a common ground in common. All three basic circuits are named after their in- and output: emitter circuit, base circuit and collector circuit.
Depending on circuit the transistor-based amplifier has different properties as shown in the table below… To compute tha amplifier factor of a circuit the dynamic input (alternate current) \$r_{BE} = h_{11}\$ and dynamic output impedance \$r_{CE}= 1: h_22\$ and the alternate current gain \$\beta = h_{21}\$
Those h-parameters where discussed and explained later - first we want to have a look at the different circuits…
Basic transistor circuits (Overview)
emitter Circuit | base circuit | collector circuit | |
Principle | |||
Schematic | |||
Current gain | \[ V_{i} = \frac{\beta * r_{CE}}{r_{CE} + R_{C}} \] (10…500) | \[ V_{i} = \frac{\beta }{1 + \beta } \] (< 1) | \[ V_{i} = \frac{\beta * r_{CE}}{ R_{E} + r_{CE} } \] (10…500) |
Voltage gain | \[V_{u} = \frac{\beta \cdot (R_{C} \parallel r_{CE})}{r_{BE}}\] (50…1000) | \[V_{u} = \frac{\beta \cdot R_{C} \parallel r_{CE}}{r_{BE}}\] (50…1000) | \[V_{u} = 1- \frac{r_{BE}}{\beta \cdot R_{E} \parallel r_{CE}}\] (<1) |
Power gain | 5000…1000 | 100…1000 | 50…500 |
Input impedance | \[r_{e} = r_{BE} \parallel R_{1} \parallel R_{2}\] (10 Ohm…5kOhm ) | \[r_{e} = \frac{r_{BE}}{\beta} \parallel R_{E} \] (< 1 Ohm…1 kOhm) | \[r_{e} = (r_{BE}+\beta \cdot R_{E}) \parallel R_{1} \] (500 Ohm…5 MOhm) |
Output impedance | \[r_{a} = r_{C} \parallel r_{CE} \] (10 Ohm…500kOhm ) | \[r_{a} = r_{C} \parallel r_{CE} \] (100kOhm…10MOhm) | \[r_{e} = r_{E} \parallel \frac{r_{BE} + R_{Generator}}{\beta} \] (10 Ohm…1kOhm) |
Phase position | 180° | in phase | in phase |
Typical applications | standard application for low frequency and high frequency amplifier | for very high frequencies (UKW, VHF, UHF) | amplifier inputs, "impedance converter", power amps |
Transistor in emitter circuit
The emitter circuit is mostly used in small signal solutions, (also for power amplifiers). It is used as handyman. The other both circuits (base and collector circuit) are only used for special occasions… The emitter circuit gains both current and voltage, it is also the circuit with the biggest power amplification. The input impedance consists of the BE-Diode and fluctuates between very small (big $I_B$ ) and big values (minimal $I_B$). The output voltage builds up on R_{L}. It is measured against the common ground (practically U_{CE}= U_{b} - U_{RL}). Thus, there is a phase lag of 180° from the input voltage to the output voltage. For "normal" amplifiers this id not very interesting. But this changes as soon as the output signal is feedback to the input again…

Transistor in base circuit
The base circuit has an extremely low input impedance, which is also minimized by the parallel connected necessary low emitter resistance. The output impedance however is very high. The current gain is always smaller 1 (<1), due to the emitter current (=I_{B}+I_{C}) which is always bigger then the current collector respectively the output current. The advantage of the base circuit is that she can manage the highest frequency. Also, this circuit has the smallest influences to the input. Thus, the typically applications are receiver for very high frequencies.

Transistor in collector circuit
The collector circuit is awarded by a high input - but low output impedance. The high input impedance is caused by the input current as well as the output current which flows over the common emitter resistor (R_{L}). A low base current calls for a \beta multiplied collector / emitter current; which is caused by R_{L}. This ends up in voltage drop over the input impedance. If a small current causes a big voltage drop at the resistor, the resistance has to be big. Without considering the base current it amounts to \beta \cdot R_{L} - The output voltage u_{2} is always smaller than then the input voltage u_{1} - its amount is the threshold voltage from the BE-Diode.If u_{1} becomes bigger, the bigger amounts the voltage drop at R_{L} becomes due to the bigger emitter current. If u_{1} drops, so u_{2} drops due to the lower emitter current.
Thus this circuit is also called emitter follower. There is no voltage gain in this circuit (u_{2} is allways smaller than u_{1}). Only the current gain gets \beta times multiplied The emitter follower is often used in amplifier inputs for his big input impedance but low output impedance.

Amplifier coupling
One amplifier stage is regularly not sufficient, and you need to put together multiple units. But doing the coupling needs a bit of thought to not shift bias points uncontrollable.
Transformer coupling
This is the oldest but in these days unconventional more or less obsolete technique. Disadvantages are price, size and weight of the transformer. Today it is seldom used for that reason. However, it has an advantage in selecting the right signals by resonance effects.
RC coupling
The RC-coupling is probably the most used technique to de-couple amplifier stages. the attentive reader will note, that the capacitor and the resistor are forming a high-pass filter which we have seen first in here… This coupling is easy anc cheap; but has the disadvantage of also being a high-pass filter shaping the signal. Very low frequencies cannot be transmitted that way…
Direct coupling
The simplest possible coupling is a coupling by wire - this is also known as direct current coupling. Here the disadvantage is that the bias points of the different amplifier stages shifts in the different stages.
The advantage is that it allows for direct current amplification; therefore it ist use in measurements and op-amp. It is also easy to implement in integrated circuits…
JFETs and MOSFETs
Compared to the electron tube, the bipolar transistor has many advantages but one significant disadvantage: it requires a control current and therefore control power. Its input resistance is low, it loads the source (e.g., antenna, microphone), and it can often only be controlled from high-impedance sources using special techniques. The electron tube, on the other hand, requires no power and can be controlled solely by the field strength of the applied control voltage. The practical significance of this is that its input resistance is very high and the source (e.g., microphone) is not loaded. No wonder, then, that a component was sought that combined the advantages of the transistor with those of the tube. The result of this development is the group of field-effect transistors (abbreviated FET). The name refers to the operating principle: the FET is controlled only by the field strength of the applied control voltage, without control current, i.e., without power (apart from leakage currents and losses). Since only charge carriers of one polarity are moved in it – either electrons or “holes” – FETs are called unipolar transistors.
Functional principle of the field-effect transistor
The principle of field-effect control is “old” compared to the bipolar transistor. As early as 1928, Julius Edgar Lilienfeld received a patent for the principle of changing the resistance of an electric field. However, this discovery could not yet be put to practical use, because an electric field does not penetrate deeply into good (metallic) conductors; although the penetration depth in insulators is very large, they cannot be used as resistors ( =conductors). The development of semiconductors provided the suitable material that conducts on the one hand and allows the electric field to penetrate deeply on the other. In 1952, Shockley was able to present the first usable FET. However, it took many years before it was ready for production.
To understand the operating principle of the FET, let us recall the following basics:
A conductor only conducts if it contains mobile charge carriers (electrons or “holes”).
The resistance of a conductor (made of the same material) increases as its cross-section decreases: the resistance of a thick copper wire is lower than that of a thin one.
Like charges repel each other, unlike charges attract each other.
The main part of the FET is a current path (“channel”) made of weakly doped silicon. Depending on whether the channel is n-doped or p-doped, it is called an n-channel or p-channel. The channel is a resistor and conducts in both directions. Its ends are called the source (abbreviated S) and drain (abbreviated D). An electrode, the gate (abbreviated G), is insulated around the channel.
The mode of operation is explained using an n-channel FET: The n-channel conducts because it contains freely moving electrons. If the gate receives a negative voltage relative to the channel (source), the electrons in the gate repel those in the channel and push them from the edge zone to the center. In the edge zone, the channel becomes a pure crystal again, i.e., an insulator. This narrows the conductive cross-section of the channel and increases its resistance. If the (negative) gate voltage is increased, more and more electrons are displaced from the channel, i.e., its conductive part becomes increasingly narrower. At a certain gate voltage (the “cut-off voltage”), all electrons are finally displaced at one point, the channel is “cut off,” and it no longer conducts.
The control also works in reverse: a very weakly doped p-channel is initially non-conductive. A positive gate voltage draws electrons into the channel and makes it conductive. The channel resistance decreases with increasing U_{GS}. '‘’ The FET is a resistor that can be controlled by the field strength of the control voltage. ‘’' The control range is very large. In principle, D and S can be swapped, but since FETs are not manufactured to be exactly symmetrical, the “correct” connection method achieves better results. Depending on how the FET principle is implemented, a distinction is made between different families of FETs. The two main groups are the junction FET (JFET) and the MOSFET.
The junction field-effect transistor (JFET)
The gate is located as a heavily doped zone around the lightly doped channel. It is doped in the opposite direction to the channel, creating a pn junction whose barrier layer acts as insulation. This group of field-effect transistors is therefore called a junction FET or JFET (J for junction).

The function is again illustrated using the n-channel FET (see image above): U_{DS} lies between D and S. The electrons flow from S to D. Now the voltage U_{GS} (negative pole at G) is applied to the gate. The pn junction between G and the channel is in the reverse direction. As with the capacitance diode, the barrier layer becomes wider as the voltage increases. Since the channel is weakly doped in relation to the gate, the barrier layer grows predominantly into the channel, i.e. the electrons are displaced from part of the channel. This part becomes non-conductive as pure crystal. The conductive part of the channel becomes narrower, its resistance increases, until the channel is “cut off” at a certain gate voltage and no longer conducts – see above. No control current flows – with the exception of the small leakage current present in all diodes. The p-channel JFET works in exactly the same way, only with reverse-polarized batteries (voltage sources).
The MOSFET
In the second group of FETs, the insulation between the gate and the channel consists of an extremely thin layer of silicon dioxide (SiO_{2}); the gate is designed as a metallic coating (vacuum-deposited Al). According to their structure, these FETs are named after the metal of the gate, the oxide of the insulating layer, and the semiconductor of the channel: MOS-FET.
In the figure above, the channel consists of weakly p-doped material, D and S of strongly n-doped islands. The substrate, the “base” of the crystal (B, from bulk = mass, main part) is connected to S internally or by external wiring.
Regardless of how voltage is applied to S and D, one of the pn junctions between the channel and the connection island is in the reverse direction. The MOSFET blocks if no voltage is applied to G. If G receives a positive voltage U_{GS}, the holes as positive charge carriers are immediately displaced from the channel area opposite the gate electrode, electrons from the substrate present with S (negative pole of the voltage source) are attracted, so that an n-conducting bridge, the “inversion layer,” is formed between D and S opposite G. The resistance of this layer decreases as U_{GS} increases. This type of MOSFET only becomes conductive when the channel region is enriched with electrons; it is therefore called an “enrichment type” and is also self-blocking because it does not conduct when the gate is open or U_{GS} = 0V. Another type is manufactured in such a way that the channel region is already weakly n-doped. When G is open or U_{GS} = 0V, it conducts; it is “self-conducting.” With negative U_{GS}, the electrons can be displaced from the channel region until they are cut off; with positive U_{GS}, electrons can be sucked into the channel area, so that the channel resistance decreases further and I_{D} increases accordingly. Control with negative U_{GS}, i.e., with the displacement of electrons, is preferred. Therefore, this family of MOSFETs is called “depletion type.” The special feature of self-conducting MOSFETs is that they can be controlled by both positive and negative gate voltages.
The other MOSFET types are derivatives of the two main groups above, which will not be described in this introduction.
Translated with DeepL.com (free version)
From the BJT to the FET
Corresponding to the basic circuits for bipolar junction transistors (BJT) the same rules apply to the Field-Effect-Transistors, introduced in this blog post. The emitter circuit is the source circuit, the base circuit ist the gate circuit and the collector circuit the drain circuit.
The gate circuit is seldom used, because the biggest advantage of the FET, the high input impedance cannot be applied with thaat.
Source circuit | Gate circuit | Drain circuit |

