Fall 2018

ECE 110

Course Notes

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An AC generator produces a sinusoidal voltage (with zero DC offset) because of its rotation. You can use diode circuits to prevent this voltage from reversing polarity; this process is called rectification and is a step towards AC to DC conversion. You can also use a diode to clip the voltage to a desired maximum value so that you can protect other connected electronic components from high voltages.

Figure 1

Sinusoidal voltage waveform
Fig. 1: Sinusoidal voltage waveform $V_{\text{in}}$. This voltage waveform $5 \text{sin}(t)\text{ V}$ could be the output of an AC generator, whose shaft is rotating at an angular velocity of 1 rad/s. Below, we treat this signal as the input to diode circuits and call it $V_{\text{in}}$.


The fact that a diode allows current to flow in only one direction means that it can rectify a sinusoidal voltage waveform by blocking its negative part.

Figure 2

Half-wave rectifier
Fig. 2: Half-wave rectifier. A half-wave rectifier circuit consists of a diode in series with a resistor. The input voltage $V_{\text{in}}$ is applied across the diode and the resistor. The output voltage $V_{\text{out}}$ is taken across the resistor.

We analyze this circuit by assuming that the diode follows the offset ideal model and we treat the diode's OFF and ON states separately.

Figure 3

Half-wave rectifier with the diode OFF
Fig. 3: Half-wave rectifier with the diode OFF. When $V_{\text{in}} < V_{\text{on}}$ in Fig. 1, the diode is OFF and is replaced by an open circuit in this figure. Now, the circuit is broken and $V_{\text{out}}=0\text{ V}$.


Figure 4

Half-wave rectifier with the diode ON
Fig. 4: Half-wave rectifier with the diode ON. When $V_{\text{in}} > V_{\text{on}}$ in Fig. 1, the diode is ON and is replaced by an element with voltage drop $V_{\text{on}}$ in this figure. Now, we apply KVL to obtain: $V_{\text{in}}=V_{\text{on}}+V_{\text{out}}$. Therefore, $V_{\text{out}}=V_{\text{in}}-V_{\text{on}}$.

Combining the results from Fig. 3 and Fig. 4 gives
\begin{equation}
V_{\text{out}} = \begin{cases}
0, & \text{if } V_{\text{in}} < V_{\text{on}}, \\
V_{\text{in}}-V_{\text{on}}, & \text{if } V_{\text{in}}>V_{\text{on}}.
\end{cases} \label{DCS-HWE}
\end{equation}

Figure 5

Half-wave rectifier input and output
Fig. 5: Half-wave rectifier input and output. The input $V_{\text{in}}$ is from Fig. 1. The output $V_{\text{out}}$ is the result of applying equation $\eqref{DCS-HWE}$ with $V_{\text{on}}=0.7\text{ V}$. In this way, the half-wave rectifier prevents $V_{\text{out}}$ from reversing polarity by blocking the negative part of $V_{\text{in}}$.



Diode circuits can protect electronic equipment from high voltages. An example is the diode clipper, which prevents its output voltage from exceeding a set limit.

Figure 6

Diode clipper
Fig. 6: Diode clipper. A diode clipper circuit consists of a resistor, a diode and constant voltage source $V_1$ in series. The input voltage $V_{\text{in}}$ is applied across all three elements. The output voltage $V_{\text{out}}$ is taken across the diode and voltage source.

Just like the half-wave rectifier, we analyze this circuit by assuming that the diode follows the offset ideal model and we treat the diode's OFF and ON states separately.

Figure 7

Diode clipper with the diode OFF
Fig. 7: Diode clipper with the diode OFF. When $V_{\text{in}} < V_1+V_{\text{on}}$ in Fig. 1, the diode is OFF and is replaced by an open circuit in this figure. Now, we apply KVL to obtain: $V_{\text{in}}=I_1R_1+V_{\text{out}}$. Note that $I_1=0$ since $R_1$ is not part of a complete circuit. Therefore, $V_{\text{out}}=V_{\text{in}}$.


Figure 8

Diode clipper with the diode ON
Fig. 8: Diode clipper with the diode ON. When $V_{\text{in}} > V_1+V_{\text{on}}$ in Fig. 1, the diode is ON and is replaced by an element with voltage drop $V_{\text{on}}$ in this figure. Now, we apply KVL to obtain: $V_1+V_{\text{on}}=V_{\text{out}}$. Therefore, $V_{\text{out}}=V_1+V_{\text{on}}$.

Combining the results from Fig. 7 and Fig. 8 gives
\begin{equation}
V_{\text{out}} = \begin{cases}
V_{\text{in}}, & \text{if } V_{\text{in}} < V_1+V_{\text{on}}, \\
V_1+V_{\text{on}}, & \text{if } V_{\text{in}} > V_1+V_{\text{on}}.
\end{cases} \label{DCS-DCE}
\end{equation}

Figure 9

Diode clipper rectifier input and output
Fig. 9: Diode clipper input and output. We set the constant voltage source $V_1=2\text{ V}$. The input $V_{\text{in}}$ is from Fig. 1. The output $V_{\text{out}}$ is the result of applying equation $\eqref{DCS-DCE}$ with $V_{\text{on}}=0.7\text{ V}$. In this way, the diode clipper clips the output voltage to a maximum of $V_1+V_{\text{on}} = 2.7 \text{ V}$.

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A full wave-rectifier uses four diodes to reverse the polarity of the negative half of the input voltage waveform while preserving the polarity of the positive half.

Figure 10

Full-wave rectifier
Fig. 10: Full-wave rectifier. A full-wave rectifier circuit consists of four diodes in a diamond configuration. The output voltage $V_{\text{out}}$ is taken across a resistor.

We assume the diodes are identical and follow the offset ideal model. Then there are three possible combinations of diode ON/OFF states depending on the value of $V_{\text{in}}$.

Figure 11

Full-wave rectifier
Fig. 11: Full-wave rectifier with $V_{\text{in}} > 2V_{\text{on}}$. The diodes $D_2$ and $D_3$ are ON and the $D_1$ and $D_4$ are OFF. Then KVL gives $V_{\text{in}}=V_{\text{on}}+V_{\text{out}}+V_{\text{on}}$. Therefore, $V_{\text{out}}=V_{\text{in}}-2V_{\text{on}}$.


Figure 12

Full-wave rectifier
Fig. 12: Full-wave rectifier with $V_{\text{in}} < -2V_{\text{on}}$. The diodes $D_1$ and $D_4$ are ON and the diodes $D_2$ and $D_3$ are OFF. Then KVL gives $0=V_{\text{in}}+V_{\text{on}}+V_{\text{out}}+V_{\text{on}}$. Therefore, $V_{\text{out}}=-V_{\text{in}}-2V_{\text{on}}$.


Figure 13

Full-wave rectifier
Fig. 13: Full-wave rectifier with $-2V_{\text{on}} < V_{\text{in}} < 2V_{\text{on}}$. All the diodes are OFF. Then the circuit is broken and $V_{\text{out}}=0\text{ V}$.

Combining the results from Fig. 11, Fig. 12 and Fig. 13 gives
\begin{equation}
V_{\text{out}} = \begin{cases}
{-}V_{\text{in}}-2V_{\text{on}}, & \text{if } V_{\text{in}} < -2V_{\text{on}}, \\
0, & \text{if } -2V_{\text{on}} < V_{\text{in}} < 2V_{\text{on}}, \\
V_{\text{in}}-2V_{\text{on}}, & \text{if } V_{\text{in}}>2V_{\text{on}}.
\end{cases} \label{DCS-FWE}
\end{equation}

Figure 14

Full-wave rectifier input and output
Fig. 14: Full-wave rectifier input and output. The input $V_{\text{in}}$ is from Fig. 1. The output $V_{\text{out}}$ is the result of applying equation $\eqref{DCS-FWE}$ with $V_{\text{on}}=0.7\text{ V}$. In this way, the full-wave rectifier reverses the polarity of the negative part of $V_{\text{in}}$ while preserving the polarity of its positive part.


A basic AC to DC converter can be made with a rectifier and a capacitor. This kind of circuit is inside most AC adapters used to power household electronic devices.

Figure 15

Disassembled AC Adapter
Fig. 15: Disassembled AC adapter. This AC adapter contains a transformer, a full-wave rectifier and a smoothing capacitor. The transformer provides the rectifier with AC voltage at lower peak-to-peak magnitude than the AC voltage that comes out of the outlet. The resistance (not pictured) is provided by the load. Image source.

The full-wave rectifier by itself would provide an output voltage that oscillates between zero and a maximum value, as shown in Fig. 14. This fluctuation is undesirable for most electronics. The role of the capacitor across the output terminals is to smooth the output voltage.

Figure 16

AC to DC converter
Fig. 16: AC to DC converter. An AC to DC converter can consist of a rectifier (in this case, a full-wave rectifier) with a capacitor across the output terminals.

One way to understand this circuit is to see that the capacitor charges when the rectifier output voltage is large and discharges when the rectifier output voltage is small.

Figure 17

AC to DC converter input and output
Fig. 17: AC to DC converter input and output. The input $V_{\text{in}}$ is from Fig. 1. The output $V_{\text{out}}$ is a smoothed version of the output in Fig. 14. The magnitude of the fluctuation that remains is called the ripple.

In ECE 210: Analog Signal Processing, you will learn how to analyze the AC to DC converter circuit in Fig. 16 mathematically. You will also see how the same circuit can demodulate a transmitted AM radio signal so that you can play the signal on a speaker.