Section B9: Zener Diodes

When we first talked about practical diodes, it was mentioned that a parameter associated with the diode in the reverse bias region was the breakdown voltage, VBR, also known as the peak-inverse voltage (PIV). This was a bad thing before – the whole avalanche breakdown, large current, overheating device and total destruction thing...

Well, guess what? Under specific fabrication conditions, a diode may be created that will not be destroyed if the breakdown voltage is exceeded, as long as the current does not exceed a defined maximum (to prevent overheating). These devices are known as zener diodes and they are designed to have an avalanche characteristic that is very steep. The IV characteristic curve and diode symbols for the regular and zener diodes are given to the right (Figure 3.38 of your text).

In the forward bias region, the zener behaves like a regular diode within specified current and/or power limits. The magic of these devices comes in when we get into the reverse bias region. As previously mentioned, the zener is designed to have an almost vertical avalanche characteristic at the breakdown voltage – hereinafter also called the zener voltage, and it is ideal for use in voltage regulation. The limiting (maximum) power for a zener diode is given by Pz=VzIzmax and is a function of the design and construction of the diode. The knee of the curve (the current for which |vD|=VZ) is generally approximated as 10% of Izmax, or Izmin=0.1Izmax.

There are two distinctly different mechanisms that may cause breakdown in a zener diode:

1. Above approximately eight (8) volts, the predominant mechanism is avalanche breakdown, also referred to as impact ionization or avalanche multiplication. This process begins with thermally generated minority carriers that acquire enough kinetic energy to break covalent bonds and create an EHP through collisions with crystal atoms. The free carriers created through this collision contribute to the reverse current and may also possess enough energy to participate in collisions, creating further EHPs and the avalanche effect. 2. The high field emission or zener breakdown mechanism is the second method of disrupting the covalent bonds of the crystal and increasing the reverse bias diode current. The reverse voltage where this occurs is determined by the diode doping and occurs when the depletion layer field is large enough to break covalent bonds and cause the number of free carriers due to EHP generation to multiply.

Either of these effects, or a combination of the two, significantly increases the current in the reverse bias region while having a negligible effect in the voltage drop across the junction. Although “breakdown” and “disruption” and words of that order have been liberally used in the previous discussion, please realize that the zener process in not inherently destructive unless the maximum power dissipation specified for the device is exceeded.

Zener Regulator

As mentioned earlier, the characteristics of the zener diode make it ideal for application as a voltage regulator. Placing the zener diode in parallel with the load as shown in Figure 3.39 (reproduced to the right) ensures an essentially constant output voltage even though the load current and the source voltage may vary. The key to the design of this voltage regulator is to choose the resistor Ri to keep the zener in the breakdown region, while ensuring that the diode current never exceeds Izmax.

Your text derives an expression for this circuit parameter by developing the nodal expression for the zener current and defining the two extremes for iZ in terms of the input/output conditions:

1. Izmin occurs when the load current is maximum and the source voltage is minimum. 2. Izmax occurs when the load current is minimum and the source voltage is maximum.

Circuit analysis techniques yield an expression for the resistor of interest as

v s − VZ in Equation 3.56, where Ri = and iR=iZ+iL. Equating the iR

characteristics for the extremes of iZ (Izmin and Izmax) in the expression for Ri yields:

Vs min − Vz Vs max − Vz Ri = = (Equation 3.58) IL max + Iz min IL min + Iz max using the approximation Izmin=0.1Izmax, stirring liberally and rearranging...

IL min(Vz − Vs min) + IL max(Vs max − Vz ) Iz max = (Equation 3.61) Vs min − 0.9Vz − 0.1Vs max

The variation in load current (or, equivalently, load resistance) and source voltage may be given or measured. Be aware that these derivations are based on the rule of thumb relationship between the maximum and minimum zener current. If another relationship is defined, you’ll have to back up to Equation 3.58 and rework Equation 3.61.

Once Izmax is known, the second expression in Equation 3.58 may be used to solve for Ri.

Equivalently, Equation 3.58 (or Equation 3.61) may be solved for Izmin by rearranging our rule of thumb to be Izmax=10Izmin:

IL min(Vz − Vs min) + IL max(Vs max − Vz ) Iz min = (Equation 3.61: Modified) 10Vs min − 9Vz − Vs max

In this case, the first expression in Equation for 3.58 may be used to solve for Ri.

One final note before we leave this topic. Be aware that it is not written in stone that every combination of source voltage and/or load current will result in a viable circuit. As illustrated in Example 3.6(b), sometimes there is no resistor Ri that will make the regulator operate correctly. As your author states, something in the design conditions will have to change – an increase in source voltage or a reduction in load current for the desired output voltage (This is obviously assuming that you are totally committed to the zener voltage!).

Full-Wave Zener Regulator

The filtering discussion in Section B7 introduced the reduction of output ripple by using a parallel RC combination. As shown in Figure 3.41 of your text (reproduced below), this process may be enhanced by introducing a zener regulator after the RC filter. Note that in the circuit above, the resistor in the RC combination is no longer the load, but is what’s known as a bleeder resistor and is denoted RF. The purpose of RF is to provide a discharge path for the capacitor if the load is the removed. It is desired that this resistor absorb as little power as possible when the circuit is in operation, so it usually has a very high resistance (higher resistance, lower current for same voltage).

Anyway, we can still use Equation 3.52 to solve for the capacitor (now called CF to match the RF notation), with, of course, a couple of modifications:

¾ In Equation 3.52, we were only concerned with the maximum swing of the source with respect to the zero axis. However, since the voltage across Ri will not go to zero as long as the zener is operating, the Vmax term is replaced by Vsmax-Vz. ¾ The equivalent resistance across the capacitor CF is evaluated under forward bias conditions and is the parallel combination of RF and Ri. However, since RF is generally very much larger than Ri, this parallel combination is approximately equal to Ri. ¾ The remainder of the terms are as defined in Equation 3.52: o ∆V is the peak-to-peak ripple allowable at the output, and o fp is the frequency of the rectified waveform (twice the original frequency for full-wave rectification).

Putting this all together, an expression for the capacitance in a full-wave zener rectifier is given by

Vs max − VZ CF = (Equation 3.62) ∆VfpRi

Practical Zener Diodes and Percent Regulation

We’ve been toodling along in this discussion acting like the zener diode is going to behave absolutely perfectly at all times – the characteristic in the breakdown region is perfectly vertical (infinite slope implies zero resistance), it’s going to give us an absolutely perfectly constant voltage as long as we don’t exceed some simple power rating, right? Well, not exactly (big surprise)...

Actually, the zener is pretty well behaved and is extremely useful if used correctly. However... to account for the fact that the curve is not perfectly vertical, we must include a nonzero zener resistance in series with our ideal diode as shown in Figure 3.42 and reproduced to the right. The effect of this resistor (RZ) is to cause the output voltage to deviate from the constant value of the ideal zener voltage (VZ’ in the figure) What we’ve got now at the output is the practical zener voltage,

VZ = VZ’+iZRZ.

Your text illustrates a numeric example of this effect in Equation 3.63. By using the two extremes of zener current (IZmax and IZmin), it can be seen that the output of a practical zener diode varies between Voutmax and Voutmin. Since we have a nonideal output, the concept of percent regulation is introduced.

Percent regulation is defined as the total variation over the nominal (desired) value. For voltage regulation of a zener diode, this translates to

V −V %Regulation = out max out min * 100 (Equation 3.64: Modified) Voutnomin al

The lower the percent regulation, the better the regulator – an ideal zener diode would have a percent regulation of zero (Voutmax =Voutmin).