## Pentode Dynamic Characteristic Curves

[01/05/2013]

**Further reading of the RDH4 showed that there are easier ways to set up the operating conditions, and to optimize the stage for either maximum voltage gain or minimum distortion, or a compromise between the two. The texts below are kept for background information only and should not be relied upon for actual designs…**

While working on a PA to guitar amp conversion project over at AX84 Forum, an interesting problem pop up. How do you draw a load line for a pentode with very low screen voltage? If you use the conventional method, the lines (if they can even be drawn) just looked strange.

Look up the RC-Coupled chart for say 6SJ7, then try to plot the load lines, you will soon see what the problem is… Well, it turned out we were doing it all wrong, the correct procedure was (as usual) clearly outlined in the Radiotron Designer’s Handbook (see below), just got to know where to look, I suppose…

Anyway, the correct method relied on the dynamic characteristic chart for the pentode, the 6J7/6C6 was used as an example in the Handbook, so far so good, but when it comes to newer tubes such as the 6SJ7 in our design, no such chart exist, at least not with curves for the low screen voltage that we are interested in. So how do we go about creating a chart like the one used in the Handbook?

The information that we are interested in is plate current (Ia) vs. control grid voltage (Vgk), with the screen voltage (Vsk) swept from say 0-100V while holding the plate voltage (Vak) steady at say 100V. I thought the curve tracer with an external supply can be used together to generated the curves. And I believe I got the right curves from the setup (still need to verify it). However, what we see on the scope is actually Ia vs. Vsk, not Ia vs. Vgk. So we still need to find a way to transpose the Vgk scale onto the Ia vs. Vsk plot.

Here you see the Ia vs Vs plot with estimated Vgk scale from the above setup (6AU6 was used for the test):

[01/10/2013]

It was there all along… just got to learn to use the tool properly. To get the Ia vs Vs plot with Vg on the X-scale turned out to be nothing more than changing the sweep parameters on the simulation run – just need to swap the step parameters around! Here is the plot for the 6AU6, and it matches up well with the datasheet. So this could still come in handy one day. I am not sure this setup could be duplicated with the curve tracer “as is” since the grid voltage output is not continuously variable but in staircase form, will take a closer look when time permits.

**Pentode Dynamic Characteristic**

Here is the relevant text from the Radiotron Designer’s Handbook:

*The Dynamic Characteristic of a Pentode* is of particular importance with resistance coupled amplifiers and will generally be found more convenient as basis of calculations than the Plate Characteristic. A typical family of Pentode Dynamic Characteristics is shown in Fig. 12, these being for type 6J7-G (6C6). The curves for all screen voltages are very similar and have a fairly rounded bottom bend, a nearly straight portion, and a fairly sharp top bend. As a detector, either the top or bottom bend may be used, the top bend being more suitable for small input voltages. As an amplifier, the operating point should be chosen so that the dynamic path does not leave the straight portion. If only small output voltage is required, there is considerable latitude in the choice of operating point without the occurrence of perceptible distortion. When the maximum possible output voltage is required the working point should be at a current of about 0.56 Eb/RL. When Eb = 250 volts the RL = 0.25 megohm this becomes 0.56 mA.

It will be seen from the shape of the curves that those corresponding to the lower screen voltages have the longest straight portions. There is therefore an advantage in selecting a. low screen voltage when a high output voltage is required. The limit to the choice of a low screen voltage is set by the occurrence of grid current (at a bias of about -0.7 volt for type 6J7-G). A screen voltage of 37 volts is a good compromise tor the conditions of Fig. 12. The final adjustment of the operating point may be made by slight alteration of either screen or bias voltage, until the plate current is 0.56 EB/RL.

Slightly higher gain may be obtained by operating at a. higher plate current, since the point of maximum gain occurs at the point of inflexion immediately below the commencement of the top bend. Only a limited output voltage is obtainable, under these conditions, before distortion appears as a result of non-linearity. The adjustment of voltage is also considerably more critical than for the centre point of the nearly-straight portion of the curve. A further reason for the choice of the lower operating point is that the distortion, even though small, is largely second harmonic, while that at the point of inflexion is largely third harmonic.

Since the plate current is also the current flowing through the load resistor, there is a linear relationship between the plate current and the plate voltage, either D.C. or A.C. Consequently the Dynamic Curves may be calibrated with a plate voltage scale in addition to plate current. In Fig. 12, for example, zero plate voltage corresponds to 1 mA, and 250 volts on the plate to zero current. Thus the gain of the valve under dynamic conditions (ΔEp/ΔEg1) is given by the slope of the dynamic characteristic.

If the swing is sufficient to operate the valve beyond the-limits of the nearly-straight portion of the curves, the gain will vary as the signal voltage is increased. For most practical purposes the ratio between the peak plate voltage and the peak grid signal voltage may be taken as the gain, since the excitation of the following stage is dependent upon the peak voltage.

When the D.C. load resistance is shunted by an A.C. load Rg, such as in the case where Rg is the grid resistor of the following valve, the gain and peak output voltage will be reduced. The modified gain under these conditions will be Rg/(RL + Rg) of the gain without any shunting. The peak output voltage will be reduced in the same proportion as the gain.

Since the curvature of the dynamic characteristic is a measure of the harmonic distortion the peak output voltage which may be delivered with limited distortion is readily calculable.

When self bias is employed, it is possible to apply the method previously given (Fig. 10) for determining the static operating point. With triodes the dynamic characteristic may he used directly as in Fig. 10, but with pentodes there must be an adjustment since the cathode current is the sum of the plate and screen currents. In this, use may be made of the fact that the ratio between screen and plate currents is nearly constant. If this constant is A, the intersection of the dynamic characteristic and a straight line from O having a slope of -1/[RK (1 + A)] will indicate the static operating point. If. for example, the published plate and screen currents are 2.0 and 0.5 mA. respectively, A will be 0.5/2 or 0.25. The cathode resistor may be 2000 ohms, but the effective cathode resistor as regards the plate current only will be 2000 (1+0.25) or 2500 ohms. If now the sloping line is drawn for 2500 ohms, its intersection with the dynamic characteristic will give the operating point.

*Screen Dropping Resistor*

In order to determine the resistance of the screen dropping resistor, it is necessary to make use of the plate characteristics of the valve as a triode, that is, with the plate connected to the screen. To a. fairly close approximation the screen current is equal to A/(1+A) of the triode cathode current (i.e., plate + screen electrode currents) where A is the ratio between screen and plate currents. The plate characteristics of the valve as a triode may therefore be used to represent the screen current-screen voltage characteristics provided that a, new scale is added for screen current in which 1mA of screen current is equivalent to (1 + A)/A milliamperes of cathode current (Fig. 13). Since a considerable change of plate voltage results in only a slight change of cathode current, these characteristics may be regarded as being independent of plate voltage.

On these curves a loadline may be drawn, the slope being -1/Rd where Rd is the resistance of the dropping resistor. The loadline drawn in Fig. 13 is for a screen supply voltage of 300 volts and a screen dropping resistance of 1 megohm. The intersection of the loadline and the corresponding grid bias curve gives the Figure 13 screen voltage. Alternatively, it the grid bias and screen voltage are known, the loadline may be drawn and the resistance calculated from its slope.

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