# What Happens When You Connect Zener Diodes in Series?

October 28, 2020

### Key Takeaways

• Zener diodes can be placed in series or parallel with other circuit elements, which includes other Zener diodes.

• When using Zener diodes in series, the current and voltage distribution will follow Kirchoff’s laws, and you can derive a specific relationship for the voltage and current distribution in your diodes.

• Back-to-back series Zener diodes enable some useful characteristics in AC circuits, thanks to their rectifying behavior.

You can connect these Zener diodes in series.

Zener diodes are fundamental semiconductor devices used in many integrated circuits. These components are simple, as they provide rectifying behavior with high transconductance when forward biased. They can be mass-produced for use in a range of systems and can be used as discrete components. In some circuits, you may want to take advantage of the rectifying behavior of Zener diodes in series to provide some useful electrical behavior. If this is done in your circuits, how does a series arrangement of Zener diodes affect electrical behavior?

The answer depends on how the Zener diodes are oriented in series—whether they are in an end-to-end arrangement or back-to-back arrangement. When you place Zener diodes in series in this way, you can use some simple applications of Kirchoff’s laws and Ohm’s law to determine the distribution of voltage and current in the series arrangement. Here’s when you might encounter Zener diodes in series and how various arrangements affect current and voltage distribution in a series circuit.

## Connecting Zener Diodes in Series

Just like other circuit elements, multiple Zener diodes can be connected in series. There are two types of arrangements for diodes in series. End-to-end arrangements are arranged in series with the cathodes facing each other, or with the anodes facing each other. In this case, one Zener diode will be forward biased while the other is reverse biased. In the end-to-end arrangement, the cathode of one diode is connected to the anode of another diode, so both will be forward biased or both will be reverse biased.

End-to-end and back-to-back current-voltage diodes in series.

The effects of rectification in each diode in series will determine how a voltage gives rise to a current in this arrangement. If you look at the Zener diode current equation, the rectifying behavior of a Zener diode causes current saturation to occur in both directions in a back-to-back Zener diode. In other words, because one diode is always reverse biased, the current will be limited to the saturation current, even in the forward biased diode. This does not occur in the end-to-end arrangement, and its current-voltage curve will look just like the typical current-voltage curve for a single Zener diode. The graph below shows how the current in the above back-to-back and end-to-end arrangements compare.

End-to-end and back-to-back current-voltage relationship for Zener diodes in series.

Because the current and voltage characteristics in end-to-end diodes are so similar to those seen in a single diode, we do not need much more investigation. Using Kirchoff’s voltage law and Ohm’s law, you can show that the voltage drops across each diode in the end-to-end configuration are equal as long as the diodes have the same ideality factor and saturation current. For back-to-back diodes, this is not the case, as we’ll see below.

## Voltage and Current in Back-to-Back Diodes

To see why this saturation behavior occurs in back-to-back arrangements of diodes, we need to look at the distribution of current and voltage in the two diodes using Kirchoff’s laws and Ohm’s law. When the back-to-back arrangement of identical Zener diodes in series is connected to a DC voltage source, the following occurs:

1. The reverse-biased diode runs in saturation, so it has the highest impedance, while the forward biased diode has the lowest impedance (due to Ohm’s law).

2. Because the reverse biased diode has the highest impedance, it has the largest voltage drop, which limits the current produced by the forward biased diode (due to Kirchoff’s voltage law).

3. As the voltage applied to the pair of diodes keeps increasing, the current in the circuit approaches the saturation current (due to Kirchoff’s current law).

In general, you can determine the voltage dropped across each diode by looking at the saturation currents and ideality factors for each diode in the back-to-back arrangement. If you use Kirchoff’s current law, you can determine the voltage drop across the reverse biased diode VB and across the forward biased diode VF. This is defined in the equation below:

Reverse bias and forward bias voltage in a back-to-back Zener diode.

This nicely summarizes the DC current and voltage behavior of two Zener diodes in series when connected in a back-to-back configuration: the voltage distribution is determined entirely by the ideality factor of the forward biased diode and the saturation currents in both diodes. Note that this behavior applies to all diodes in series, not just Zener diodes in series. The difference between Zener diodes in series and some other diodes is their breakdown voltage and reverse current during breakdown, and the current-voltage characteristics will resemble those seen in a single diode during breakdown.

## AC Current Limiting in Back-to-Back Diodes

The rectifying behavior seen in reverse biased single diodes causes saturation of an AC signal, which then limits the current that can be sent into a circuit in reverse bias; this is the basis for rectifier bridges. If you’re using a back-to-back arrangement of Zener diodes in series, you can create a current limiter that provides a clipped AC wave.

The effects of rectification in a back-to-back diode can be used to create a clipper circuit. The example below shows a clipper with a 20 Hz input sine wave. The output is taken across the series diode arrangement and is plotted in the time domain, as shown in the circuit and graph below.

Double clipping Zener diode circuit.

If you have access to a SPICE package, you can use standard diode models to generate a similar graph as that shown above. This is done with transient analysis, which will show you the variation in the AC current in a circuit in the time domain when the current is driven with an AC voltage. This mimics the behavior of a Zener-diode based voltage regulator by extending rectification to positive and negative portions of the input AC waveform. You could then feed this clipped signal into another circuit, like a comparator, to generate a clean square wave.

Once you’ve designed circuits with Zener diodes in series, you can use the best PCB layout and design software to capture your designs as an initial PCB layout. Allegro PCB Designer includes the features you need to layout boards for any application. You can then use Cadence’s analysis tools to simulate and analyze the behavior of your power electronics.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts

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