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**ELECTRONIC TRIODES "SUITE"**

**1. 3. - Differential Parameters of the Triode : **

In all the remarks made so far, we have always referred to the ** triode ECC82 ;** by studying other types of triodes, one would obtain different results, even by operating these tubes under the same conditions as the **triode ECC82.**

For example, with the same variation of the gate voltage, it would be possible to obtain a variation of the anode current higher or lower or, with the same variation of the anode current, one could obtain a variation of the anode voltage more or less strong; the gain could also be different.

Each type of triode is characterized by means of quantities capable of indicating its possibilities when it operates under given conditions, that is to say with a given gate bias voltage, a given anode current of rest and anode voltage of rest given.

For each type of triode, three quantities are indicated, called **differential parameters of the triode ;** each of them is defined by the variation of two of the three electrical quantities relative to the triode (gate voltage, anode current, and anode voltage), while the third remains constant.

A first parameter is called **PENTE** of the triode (symbol **S**), or transconductance or mutual conductance **;** this parameter indicates how much the anode current varies when the gate voltage varies by **1 V**, while the anode voltage remains constant.

If, in milliamperes, the variation of the anode current corresponds to the variation of **1 V** of the gate voltage, the slope is expressed in **milliamperes per volt** (symbol **mA / V**).

The slope allows to know the efficiency of a triode to control the anode current by means of the gate voltage **:** between two types of triodes which have different slopes, the one with the highest slope will be the best.

The slope of a triode can be determined experimentally with the circuit of Figure 13-a.

For this purpose, the gate voltage is adjusted so that the triode operates under the desired conditions and the milliampemeter reads the value of the anode current flowing through the tube.

Then the potentiometer slider is operated by varying the grid voltage by **1 V** and the value of **the anode current is read again on the milliammeter :** the difference between this value and the preceding one obviously indicates how much the anode current has varied when the gate voltage has varied by **1 V** and thus gives directly the slope of the tube.

During this test, the anode voltage does not vary because there is no anode resistance that can produce voltage variations **;** the small internal resistance of the milliammeter inserted in the anode circuit can be considered negligible.

As previously seen, it is also possible to control the current of a triode by means of the anode voltage, leaving the gate voltage unchanged.

The second differential parameter indicated for a triode makes it possible precisely to know the effectiveness of the tube to control the anode current by means of the anode voltage.

This parameter is called **the internal resistance of the triode** (symbol **r**) **:** it indicates the resistance of the tube as a function of the necessary anode voltage variation, to obtain an anode current variation of **1 mA**, the gate voltage remaining constant.

If the variation of the anode voltage necessary for the anode current to vary by **1 mA** is expressed in volts, the internal resistance is expressed in kiloohms.

The internal resistance can also be experimentally determined by means of the circuit of Figure 13-b.

For this, the triode is operated in the desired conditions by adjusting its anode voltage, which reads the value on the voltmeter.

The anode voltage therefore varies until the anode current has varied by **1 mA :** the value of the anode voltage is then read again on the voltmeter **:** the difference between this value and the value read previously indicates how much the anode voltage had to vary to vary the anode current by **1 mA** and thus directly gives the internal resistance of the triode.

Previously, we saw that the gate controls the anode current more efficiently than the anode, being closer to the cathode **: the third differential parameter** indicated for a triode makes it possible precisely to know how much the gate is more efficient than the anode for check the anodic current.

This parameter is called **the amplification coefficient of the triode** (symbol **ρ**) **:** it indicates how much the anode voltage must vary to maintain the constant anode current despite a variation of **1 V** of the gate voltage.

To have a more precise idea of this parameter, one must see how one proceeds to determine it experimentally.

For this we use the circuit of **Figure 13-c** **:** after setting the gate voltage and the anode voltage so that the triode operates in the desired conditions, read the values of the anode current and the anode voltage.

Then the gate voltage is varied by **1 V** and thus the anode current also varies by a certain amount **;** the anode voltage is then varied until the anode current returns to its initial value: the variation of the anode voltage necessary to obtain this directly indicates **the amplification coefficient of the triode.**

Unlike the other two parameters, the amplification coefficient is only expressed by a number.

Since the three differential parameters of the triode all concern the control of the anode current by the gate voltage or the anode voltage, it can be supposed that there is a relation between these three parameters **:** it has indeed been found that the coefficient of amplification is equal to the product of the slope by the internal resistance.

The differential parameters of a triode can also be determined graphically by means of the mutual and anode characteristics of the triode.

Figure 14 shows, for example, how the slope of a triode of the type ECC83 can be obtained from **its mutual characteristics.**

Let us suppose that the triode is in the rest conditions indicated by the point **Po**, that is to say with a bias voltage **Vgo = -2 V**, an anode voltage **Vao = 250 V**, an anode current of rest **Iao = 1.2 mA.**

Since the slope is given by the variation of the anode current following the variation of **1 V** of the gate voltage while the anode voltage remains constant, we consider the values taken by the anode current which correspond to the values of **- 1.5 V** and **- 2.5 V** of gate voltage.

The variation of **1 V** of the gate voltage is thus obtained by increasing and decreasing by **0.5 V** the value of **- 2 V** of the bias voltage.

From the points of the horizontal axis which have the values of **- 1.5 V and - 2.5 V,** two vertical lines are drawn up to the intersection at the points **P'** and **P"** with the relative mutual characteristic at the anodic voltage of **250 V**, on which is also the **Po** point.

Thus the anode voltage does not vary, because at the three points corresponding the same value of this voltage, while the anode current varies **:** it is seen that at the points **P'** and **P''**, the current takes the values of **2,2 mA and 0.5 mA.**

The difference between these two values (**2.2 - 0.5 = 1.7**), indicating how much the anode current varies when the gate voltage varies by **1 V**, gives the slope of the triode directly **:** it can be concluded that the triode studied, in the rest conditions indicated by point **Po**, has a slope of **1.7 mA / V.**

It is also possible to deduce the slope of the triode from the anodic characteristics of the tube, proceeding as in Figure 15.

In this case, the point **Po**, which indicates the quiescent conditions of the triode, is on the anode characteristic relative to the gate voltage **Vg = -2 V**, in correspondence with the anode voltage of rest **Vao = 250 V** and with the anodic quiescent current **Iao = 1.2 mA.**

From the point **Po**, a vertical line is drawn up to the intersection at the points **P'** and **P''** with the anode characteristics relating to the grid voltages of **-1.5 V** and **-2.5 V**, so that that in this case again, the variation of **1 V** of the gate voltage is obtained by increasing and decreasing by **0.5 V** the value of **- 2 V** of the bias voltage.

Thus, the anode voltage does not vary because at the three points still corresponding the same value of **250 V** of this voltage, while the anode current varies.

In this case again, in fact, the current corresponding to the points **P'** and **P"** takes the values of **2.2 mA and 0.5 mA**, and the difference still gives a slope of a value of **1.7 mA / V.**

This second method for finding the slope of a triode can be adopted when the mutual characteristic traced for the value of the desired anode voltage is not known **:** indeed, on the anode characteristics, it is possible to follow the graphical resolution of the slope which that is the value of the anode voltage, which one reads directly on the horizontal axis.

With these same anode characteristics, one can also find the internal resistance of the same triode, proceeding as in Figure 16.

In this case also, the point **Po** indicates the conditions of rest of the triode, which are the same as those which we already studied previously.

Since the internal resistance is given by the variation of the anode voltage necessary to obtain the variation of **1 mA** of the anode current while the gate voltage remains constant, we study the values that the anode voltage must take to vary the anode current between the values of **1.7 mA and 0.7 mA**, that is to say to increase and decrease by **0.5 mA** compared to the value of **1.2 mA** of the anode current quiescent.

From the points of the vertical axis which indicate the values of **1.7 mA and 0.7 mA**, two horizontal lines are drawn up to the intersection at the points **P'** and **P''** with the anodic characteristic relative to the grid voltage of **- 2 V**, which also has point **Po.**

Thus the gate voltage does not vary because at the three points corresponds the same value of this voltage, while the anode voltage varies and goes from the value of **277 V**, which corresponds to the point **P'**, to the value of **218 V**, which corresponds to the point **P''.**

The difference between these two values (**277 - 218 = 59**), indicating how much the anodic voltage must vary so that the anode current varies by **1 mA**, gives directly the internal resistance of the triode **:** it can therefore be concluded that the studied triode in the rest conditions indicated by point **Po** has an internal resistance of **59 kΩ.**

By means of the anode characteristics of the triode, one can also find its amplification coefficient, proceeding as in Figure 17, in which the point **Po** still indicates the same rest conditions as those studied in the previous cases.

Since the amplification coefficient is given by the variation of the anode voltage necessary to keep the anode current constant when the gate voltage varies by **1 V**, the values to be taken by the anode voltage are studied so that the anode current remains unchanged value of **1.2 mA** when the gate voltage varies by **0.5 V** from the **- 2 V** value of the bias voltage, from **- 1.5 V to - 2.5 V.**

From point **Po**, a horizontal line is drawn until it meets point **P'** and **P''** with the anode characteristics relating to the gate voltage of **- 1.5 V and - 2.5 V.**

Thus, the anode current does not vary because at the three points corresponds the same value of **1.2 mA** of this current, while the anode voltage must vary to compose the variation of the gate voltage **:** we see in fact that the anode voltage reaches the values of **200 V** and **300 V** indicated in correspondence with **the points P' and P''.**

The difference between these two values (**300 - 200 = 100**), indicating how much the anode voltage must vary to keep the current constant when the gate voltage varies by **1 V**, gives directly the **amplification coefficient** of the triode **:** It can therefore be concluded that the triode studied, under the rest conditions indicated by point **Po**, has an **amplification coefficient equal to 100.**

It can then be verified that the amplification coefficient thus obtained is equal to the product of the two other differential parameters of the triode previously determined.

As the slope has a value of **1.7 mA / V** and the internal resistance has a value of **59 kΩ**, we obtain **: 1.7 x 59 = 100,3.**

The result is acceptable, because with the graphical methods, one always makes small inaccuracies which come from the difficulty to read with accuracy the values reported on the axes of the diagrams **:** for the same reason, one can sometimes note a small difference between the parameters determined graphically and those found experimentally indicated by the tube manufacturers.

The data relating to the triode studied can be indicated in this way **:**

Anode voltage of rest** :**
**Vao = 250 V
**

Anodic current of rest** :**
**Iao = 1,2 mA
**

Polarization voltage **:**
**Vgo = - 2 V
**

Slopes **: **
**S = 1,7 mA / V
**

Internal resistance** : ****r
= 59 kW**

Coefficient of amplification **:
**
** µ = 100.**

It is noted that with the three differential parameters, it is always necessary to indicate the data relating to the operating point (**anode voltage, anode current and bias voltage**) because the differential parameters of a triode are different according to the point of operation of the tube, because the features are not straight lines but curves.

Consequently, it would suffice to choose on the anode and mutual characteristics another point **Po** and to repeat for it the same operations as those of **Figure 14**, **Figure 15**, **Figure 16**, and **Figure 17** **:** it would thus be found that the values of the differential parameters are indeed different.

In the next theory, **we will study the astable multivibrators, monostable, bistable triode electronic tubes**, **we will also study the astable, monostable and bistable multivibrators based on transistors.** These operate in the same way as the triodes, except that the voltages are much lower.

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