Ideal Diodes#

An ideal diode is an idealization of a diode which perfectly prevents the flow of current in one direction, while allowing arbitrary currents in the other.

Definition: Ideal Diode

An ideal diode is a one-port with the following V-I characteristic:

\[\begin{aligned}i & = 0 \qquad \text{when} \qquad v \le 0 \\ v & = 0 \qquad \text{when} \qquad i \ge 0 \end{aligned}\]

I-V of Ideal Diode

Notation

The following symbol is used for ideal diodes:

Ideal Diode Symbol

Of course, ideal diodes do not exist in practice, but they can be closely approximated by other, existing electrical components.

Example: Ideal Diode via Op-Amp

An ideal diode can be constructed using an ideal operational amplifier and a p-n diode:

Ideal Diode via Op-Amp and pn-Diode

As long as the ideal op-amp is operated in its linear region, the above circuit behaves like a short circuit (\(v=0\)). When the op-amp saturates, the circuit behaves like an open circuit (\(i=0\)). This results in the characteristic behavior of an ideal diode:

\[ \left\vert\begin{aligned} v &= 0 \quad \text{for } i \le 0 \\ i &= 0 \quad \text{for } v \le 0 \end{aligned}\right. \]

To ensure that the ideal op-amp is operated in its linear region, the input current must be positive (\(i > 0\)), forcing the internal diode to conduct.

We can see this by analyzing the network.

Linear region (Conducting State):

When the input current \(i\) is positive (\(i > 0\)), the voltage at the inverting terminal \(v_{-}\) tends to rise. The ideal op-amp reacts by driving its output voltage \(v_{\text{out}}\) negative. This forward-biases the internal diode (Anode at \(v_{-}\), Cathode at \(v_{\text{out}}\)), closing the feedback loop.

When the feedback loop is closed, the op-amp operates in its linear region, ensuring \(v_d = 0\), i.e., \(v_{-} = v_{+}\).

According to Kirchhoff's voltage law, since the non-inverting terminal is grounded (\(v_{+} = 0\)), we have:

\[ v = v_{-} = v_{+} = 0 \]

Therefore, for any positive current \(i\), the voltage across the port is maintained at zero. The current \(i\) flows through the diode and sinks into the op-amp output.

Saturation region (Blocking State):

When the input voltage \(v\) is negative (\(v < 0\)), the potential at the inverting terminal is lower than the non-inverting terminal (\(v_{-} < v_{+}\)).

The ideal op-amp amplifies this difference, driving the output voltage to its positive saturation limit (\(v_{\text{out}} = +V_{\text{sat}}\)).

We can analyze the voltage across the internal diode:

\[ v_{\text{diode}} = v_{\text{anode}} - v_{\text{cathode}} = v - V_{\text{sat}} \]

Since \(v < 0\) and \(V_{\text{sat}} > 0\), the diode voltage is strictly negative (\(v_{\text{diode}} < 0\)). Consequently, the diode is reverse-biased and blocks current.

According to Kirchhoff's current law, the input current is the sum of the current entering the op-amp inputs and the diode current:

\[ i = i_{-} + i_{\text{diode}} \]

However, \(i_{-}\) is zero for an ideal operational amplifier, and \(i_{\text{diode}}\) is zero because the diode is reverse-biased. Therefore:

\[ i = 0 \]

Thus, whenever \(v < 0\), the circuit acts as an open circuit.