The Zener diode stabilizer circuit is well-known (fig. 1). The circuit provides practically a fixed stabilized voltage (which cannot be modified from the outside) having the voltage value of the Zener diode and has a low stabilization coefficient (<100). Being a stabilizer with parallel type adjusting element it is uneconomical for wide-range variable load (the stabilizer has high current consumption regardless of the load current value) and is used only at low load current (at most several hundred me).

The circuit calculation consists in determining the limiting resistance RL. This resistance must allow the operating point of the diode to be maintained in the stabilizing region under the conditions of variation of the supply voltage of the circuit and of the current through the RS load. The voltage source U1 can always be represented and known by its voltage at empty E0 and its internal resistance Ri, which facilitates the calculation of this circuit:

In practice, two cases usually appear related to the initial data of the calculation. The most common case is the one in which the circuit is powered from an existing source. The second case is the one in which the power supply can be adopted.

An eventual capacitor C at the output of the stabilizer circuit could increase the splitting effect (on RL and rz) of the supply voltage pulses (if any) by shunting rz with the reduced capacitor reactance. Also the variations of the output voltage can be reduced due to variable components of the load current, by decreasing the output resistance of the stabilizer for high frequencies.

At the same time, it is possible to use two or more Zener diodes with dynamic resistance and reduced temperature coefficients in series to achieve a Zener diode of higher voltage. Zener diodes with minimum temperature coefficient are those with UZ about 5.6V, and with minimum dynamic resistance are those with UZ ≈ 6.8 ... 8.2V. To increase the power dissipated by a Zener diode, if we do not have a proper Zener diode, we can use Zener plus bipolar transistor configurations, as I will show throughout this article.

**1. Design of the stabilizer in case of an imposed source**

Initial data:

- the average value of the voltage on the Us load and the indication whether it can have the typical dispersion given in the catalog for the corresponding Zener diode;
- imitations of variation of the current of the load when it is fed to the voltage Us: Is_min, Is_max and the indication if they depend on the voltage on the load;
- the limits of variation of the empty supply voltages: E0min, E0max;
- internal resistance of the power supply: Ri;
- the total permissible variation of the voltage on the load due to the variation of the supply voltage E0 and the load current IS: sUsmax.

The average value of the voltage on the load should normally be adopted close to the nominal values of the voltages on the fabricated Zener diodes. Unfortunately, these voltages can only be used as starting values in calculations, because they are defined in the catalog at certain currents, or the actual currents by diodes in the stabilizing circuits are known only after the design is completed. This situation occurs especially when it is not possible to sort the stabilizing diodes (on a standard product or in the absence of a measuring device).

If during use of the stabilizer it is possible to remain without load (empty) must be imposed Ismin = 0. Otherwise, the stabilizer may accidentally remain empty and the Zener diode may be destroyed. In order to prevent the use of the empty stabilizer, if this is done on a printed circuit separately from the load circuit, a properly sized resistor parallel to the Zener diode (to ensure Ismin) ).

If the circuit is supplied from a rectifier, then above the voltage E0min (where Smin is the stabilization coefficient). the pulses overlap. These do not practically affect the operation of the diode because they are reduced by approx. S _{min} (where S _{min} is the stabilization coefficient. The total variation of the voltage on the load ∆Usmax is the variation that appears after the circuit is made (for a given diode and a resistance, the dispersion and the tolerance do not intervene anymore).

**2. Stabilizer design**

In order to calculate the RL limitation resistance and to check the stabilizer quality, the following steps must be completed:

**a). ** A Zener diode with the nominal voltage Us close to the given Us voltage and with the limit currents meeting the approximate condition is adopted:

Sometimes the limits of the current through the Zener diode are missing. The maximum current can be determined with approximation to the relation:

where PdMAX [W] represents the maximum dissipated power of the diode, given in the catalog only for an average ambient temperature of -20 ... 300C and Uzmax is the maximum possible value of the voltage on the diode due to the manufacturing dispersion. The minimum current will be established based on the table in the catalog, depending on the stabilization demands (at low currents the dynamic resistance of the Zener diodes is higher and the lower stabilization).

For better stabilization, it is advisable to adopt an IzMIN current equal to the current from which the dynamic resistance is approximately constant and low. This current is generally:

By sorting, we can often find Zener diodes with IzMIN noticeably smaller than the above value.

The limits of the Uz voltage due to the manufacturing dispersion are read from the catalog: Uzm (minimum) and UzM (maximum). If the dispersion of the Uz voltage given in the catalog is not allowed in a specific application, it is necessary to select, for the practical realization or even before the calculations are made, the diodes that present in the middle of the current range IzMAX - IzMIN Uz voltage as close to the Uz voltage. imposed.

**b).** Since, in order to simplify the calculations, in the continuum the voltage-current characteristic of the Zener diode will be considered linear (with constant dynamic resistance), it is necessary to specify the coordinates of a point of it ("unknown point"): Iz and Uz as well as the value of the resistance dynamic rz. The known point can be retrieved from the catalog, in which case Uz has the limits of Uzmin and Uzmax, due to the manufacturing dispersion. For a series production of the circuit is practically the only solution, instead, for the achievement of unique ones, the Zener diodes can be selected and measured.

**c). ** If it is specified in the design data that Ismin and Ismax also depend on the supply voltage (the load behaves like a linear resistance), the limits of the equivalent load resistance are determined:

Because the current limits have been given to load the voltage at the US voltage.

**d). ** The limit values of the resistance RL with the relations are determined:

If the Zener diodes are selected and the Uz voltage from the known point does not show dispersion, then in the above relations it is considered:

If it is specified in the design data that Ismin and Ismax do not depend on the Us supply voltage, then the computational relations (6) and (7) become:

In order for the problem to have a solution, in both cases it must result:

If this condition is not met, the adopted Zener diode does not have the maximum current sufficiently high for the application to be resolved and a diode with the same voltage U _{z} must be adopted , but with the value of current I _{zMAX} higher (with higher P _{dMAX} dissipated power immediately).

**e). ** If the condition (11) is met and the two resistances are approximately equal, then R _{L} will be adopted with the tolerance "t" very low (1%), of the nearest normalized value, in case of series production of the circuit or even select the resistance of the value resulting in calculations, in case of unique ones.

If the two limits are noticeably spaced, it is recommended to adopt the normalized RL resistance as close to the RLMAX (without exceeding this by the positive tolerance), when the main performance of the stabilizer - the stabilization coefficient is optimal and the current through the Zener diode is within an area close to IzMIN (less power dissipated per diode).

**f). ** The performances of the stabilizer are calculated:

- the stabilization coefficient:

with:

- output resistance:

**g). ** The maximum total voltage variation produced by the variation of supply voltage and load current is determined:

which must be smaller than the one imposed on the initial data of the project. Otherwise it will be necessary to either select the Zener diodes with lower rz dynamic resistance, or to adopt a Zener diode with higher dissipated power - which has a lower dynamic resistance - but which consumes a higher current from the power supply (it is not an economic solution).

**h). ** In order to stabilize the medium voltage on the load, one of the current limits is determined by the Zener diode, for example Izmin, in the absence of the Uz voltage dispersion:

where:

with "t" = tolerance of the limitation resistance adopted, in percentages and:

**i). ** Determine the voltage on the diode without dispersion at the Izmin current:

Calculate the average voltage on the load without taking into account the dispersion:

This being also the average tension on the load, it will be compared with the value Us initially given by making a decision on its acceptance. Some increase in Uzmed voltage can only be achieved if the RLMAX is significantly higher than the RLMIN and the RL close to RLMAX has been adopted. In this case, the RL is closer and the RLMIN is adopted.

**k). ** The extremes of the US voltage are determined taking into account the dispersion and the variation. The possible dispersion of the Uzmed voltage is the same as the dispersion of the Uz voltage given in the catalog (if the diode is not selected). So the voltage at the output of the stabilizer can be between the values:

which includes both the dispersion effect and the variation due to the modification of the voltage E0 and the load current Is. It is also possible to include simple and the effect of varying the voltage Us extremes of ambient temperature to the normal temperature on the voltage U _{zmed} .

**it). ** Check if can operate in the hollow stabilizer in the case of the initial data I _{smin} different from 0. For this condition to be fulfilled:

with:

**m). ** The nominal power of the resistance R _{L is established }:

**3. ****Design of the stabilizer where the source can be adopted**

It is possible to establish a program of calculations by which to adopt the stabilizing diode and obtain the voltage E _{0} and the resistance R _{L} , starting from the maximum allowed total variation of voltage on load (excluding dispersion). As long as this calculation occupies a significant space, it will no longer be presented.

One solution that uses the calculations from the previous case is to adopt a diode with the right voltage, with a current domain:

and determining a voltage E _{0} which has the limits that meet the condition given by formula (1). The internal resistance Ri of the source can be adopted provided that a relative voltage drop λ = 0.1 ... 0.2 (as in rectifiers) occurs on this one:

In continuation the calculations can be carried out as in the previous case, resuming with an increase of the voltage E0 if the total variation of imposed voltage is not realized or with a possible reduction of it if a total variation is obtained much greater than the imposed one. In case the stabilizer will be supplied from a rectifier, the voltage Ur0 and the current Ir0 are required for its calculation. For this purpose relations are used:

where λ is determined from the relation (26) using the current denominator Izmax + Ismin when the stabilizer will not operate normally in the empty or Izmax0 otherwise. Izmax current can be calculated using the correspondingly modified (16), (17), (18) relations.

**Increasing the load current**

From the above, it turns out that the Zener diode also consumes electricity from the source, which depends on the current through the Iz diode and on the stabilized voltage. This is why a quite varied range of Zener diodes are manufactured, which differ not only by the stabilizing voltage (Uz), but also by the maximum current it supports, respectively the maximum power output that is the product between the maximum current supported by the IzMAX diode and the voltage. Maximum zener UzM.

The most commonly encountered Zener diodes support 1W power, which for an ordinary 10V diode (example: PL10Z, 1N4740 etc) means a maximum diode current of only 100mA, a value that in some situations is not satisfactory. Zener diodes are also made of tens of watts but unfortunately they are quite expensive.

If, however, we want to achieve a stabilizer like the one in Fig. 1 for larger currents, what to do?

One possibility would be to connect several Zener diodes of the same type in parallel. This is not a recommended solution, because, besides the economic aspect, the inherent dispersion of the diode parameters would adversely affect the stabilization and the currents through those diodes would be unevenly distributed. However, there is a simple, better and very cheap solution. Thus, realizing an assembly like the one in figure 2a, a Zener diode results, whose maximum dissipation multiplies approximately with the amplification factor in current β.

For example, a transistor of type 2N3055 having β ≈ 30, using a Zener diode with Pd = 1W, can obtain an equivalent diode that will be able to dissipate a power of about 20W. The stabilization will be the better the β the greater. Therefore, there is the temptation to choose transistors with β as high as possible, but the choice of the transistor is not made first by the value of the amplification factor in the current, but by the current and the maximum power dissipated by it. If in the above example a BC109 transistor, which can have β ≥ 500, a diode of more than 500W, theoretically, this transistor cannot withstand a 100mA base current and no 500W dissipated power. .

Figure 2 presents three variants for the proposed purpose. Regarding Figure 2a, it should be mentioned that if the load current decreases below the value of the minimum diode opening current (IzMIN), in order to maintain the stabilization performance it is indicated to mount a resistor between the base and the transistor emitter as in figure 2b, of which value is determined by the relation:

The need to install the transistor on a suitable radiator, if any, should not be overlooked. The equivalent Zener diode, obtained according to the diagram in Figure 2a, is frequently used in overload protection mountings, by limitation, or as a safety, if the ballast resistor (RL) is replaced by a fuse. The use of the diode-transistor combination, presented above, has another advantage. Zener diodes have a positive temperature coefficient and the base-emitter junction of the npn silicon transistors has a negative temperature coefficient. A judicious choice of these components, and especially the optimal choice of the current through the transistor (because the value of the temperature coefficient depends on this current), allows to achieve an equivalent diode almost perfectly thermally compensated.

**Increasing the stabilization factor in Zener diode**

stabilizers The simplicity of **Zener diode** stabilizers "is paid" by more modest performances than in the case of integrated stabilizers or error amplifier schemes. However, a considerable improvement in performance can be achieved very simply, using two (or more) circuits (see fig. 1) in cascade.

Thus, if the variation of the output voltage, relative to the variation of the input voltage for the first floor can be written:

then for the two floors we will have:

where Rd1 and Rd2 are the dynamic resistors of the diodes, which are usually much lower than RL1 and RL2. So the value of the report will be considerably lower. Of course, the Zener voltage of the first diode will have to be higher than the second and the larger this difference, the more RL2 will have to be higher, so the stabilization will be better.

The disadvantage of the solution lies in the need to have a primary source of higher voltage and to decrease the efficiency, because on the RL2 resistance an additional dissipation will occur.

**Design example**

To dimension a Zener diode voltage stabilizer that provides a Us = 6V voltage, with the dispersion according to the catalog, for a load that can be considered resistive having: Ismin = 10mA, Ismax = 80mA. The supply voltage is obtained from a rectifier having a nominal (external) output characteristic as in Fig. 3 (Ri = Rir = ∆ur / ∆ir = 3V / 0.15A = 20 Ω).

The voltage of the network, therefore also the voltage E0, shows variations of +/- 7%. The total variation of the voltage on the load (excluding the dispersion) is maUmax = 0.3V. The circuit is intended for a large series product that will work at the normal ambient temperature. A stabilizing diode of type 1N4735 with IzMAX = 146mA, Uzm = 5.58V and UzM = 6.82V is provisionally adopted.

It is calculated:

The limits of the empty voltage of the source are determined:

The fulfillment of the condition given by the formula (2) is verified:

So the diode corresponds in principle to the given application. The following data are extracted from the datasheet for diode 1N4735: Uz = 6.2V at current Iz = 41mA, rz = 2 Ω and PdMAX = 1W.

The load resistance limits are:

The permissible limits for the resistance R _{L} are determined :

Because RLMAX> RLMIN, the problem has a solution.

The maximum permissible tolerance of the RL resistance is then determined:

Normalized resistors can be adopted: RL = 133 Ω, tolerance ± 1% or RL = 137 Ω, tolerance ± 1%. In order to have a better stabilization I will adopt the higher value, namely 137 Ω. The minimum value of the limiting resistor RL shall be:

The performances of the stabilizer are:

which is a very good value for a Zener and Rieş≈ diode stabilizer rz = 2 Ω. The maximum total variation of load voltage (excluding dispersion) is determined:

The resistance is calculated:

The minimum diode current in the absence of dispersion is:

The voltage on the diode at this current, without dispersion, will be:

Medium tension on load, without dispersion:

which is close to the value Us = 6V imposed in the statement and can be accepted.

The extremes of the load stabilizer voltage are:

Check that the stabilizing diode supports the current that appears when the stabilizer is running empty:

The nominal power of the RL resistance is established:

A rated power resistance of at least 3W shall be adopted. Capacitor value of capacitor C is calculated by the formula:

We will choose a normalized capacitor of 680uF with the characteristic nominal voltage greater than Usmax = 6.958V, for example: 10V. When we do not have 137 Ohm resistors we can call in parallel several resistors, equivalent to the adopted value (137 Ohms), higher ohmic resistance and less dissipated power per piece but with the sum of the powers dissipated by each resistance normalized equal to min. 3W.

**Bibliography:**

*Dumitrescu M.* - Voltage and current stabilizers ", Technical Publishing House, Bucharest, 1965;

*Cătonanu, VM* - Electronic Technology", Didactic and Pedagogical Publishing House, Bucharest, 1981;

*V. Vulpe et al* - "Dioda Zener", Technical Publishing House, Bucharest, 1975.

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