# Penetration (electrical engineering)

The penetration in electrical engineering refers to the effect of a change in anode voltage on the anode current in electron tubes . It is a dimensionless quantity and is given in the literature as a percentage .

Penetration is one of the three parameters in Barkhausen's tube formula that fundamentally describe the behavior of an electron tube .

${\ displaystyle D = - \ left [{\ frac {\ partial U_ {g}} {\ partial U_ {a}}} \ right] _ {I_ {a} = {\ rm {constant}}} \ approx - \ left [{\ frac {\ Delta U_ {g}} {\ Delta U_ {a}}} \ right] _ {I_ {a} = {\ rm {constant}}}.}$

The penetration describes how much the grid voltage has to be adjusted so that a change in the anode voltage does not affect the anode current. The penetration can be constructed from the family of output characteristics. The changes in the two voltages are to be assumed to be differentially small.

In practice a pipe having a control grid with a large winding pitch greater penetration than a narrow, wound so with little pitch grating. The term penetration is superfluous for the circuit analysis and is completely replaced by the slope, not least because of its poorly descriptive definition.

The conversion between penetration and slope is carried out using the above formula, which is incorrectly attributed to Heinrich Barkhausen . This does not mean any tube-specific description, but rather the conversion of the control parameter of a controlled voltage source into the control parameter of a controlled current source . The internal resistance R i mediates between penetration D and slope S , which can also be read as a differential quantity from the output characteristic curve field.

## Inclusion in the general description of amplifier quadrupoles

The penetration D is to be assumed as a control parameter for a controlled voltage source operating in the signal direction on the output side. Strictly speaking, it is not the penetration itself that should be used as the control parameter, but its reciprocal value µ .

The above-mentioned slope S , which is to be used as a control parameter precisely when a controlled current source is assumed on the output side, is completely synonymous . In principle it is the same for the circuit designer whether he uses a controlled voltage source or a controlled current source on the output side. In general - and therefore also for electron tubes - it is common today to use a controlled current source at the output of the active quadrupole.

It is important to know that all differential quantities (in particular penetration, steepness and internal resistance) only apply to a specifically selected operating point. In the case of electron tubes, such a typical operating point is specified in the data sheet, and all differential quantities listed there relate to precisely this operating point and the specified operating frequency.

## Differentiation between penetration and retroactive effect

The penetration D must be strictly differentiated from the voltage feedback V r or the backward slope S r , since the penetration D has nothing to do with the feedback from the signal output to the signal input. The penetration D is just another expression for the steepness S , as described above.

The reverse slope S r, on the other hand, describes the change in the input current when the output voltage changes, the input voltage being kept constant. In principle, every active component in which the control electrode picks up part of the output current has such a reaction from the output to the input. The reverse steepness S r can be converted into the voltage reaction V r by means of the input resistance R e .

In the case of electron tubes, S r = 0 can be set, provided that an operating point is chosen at which practically no measurable grid direct current flows. However, if the grid bias voltage is close to 0 V, then the grid current can be measured and thus also the backward slope S r .

In the description of the bipolar transistors, the symbols V r and unfortunately also D are used for the voltage feedback. However, this is not about penetration. The voltage feedback V r , like the reverse steepness S r , is a direct measure for the feedback of a signal from the output of the circuit to the input. S r and V r can also be determined for electron tubes by recording the complete set of input characteristics, provided that a grid current can be measured. Otherwise these sizes are not available.

Another possibility of confusion is the presence of capacitances between the electrodes. The sizes penetration, steepness, voltage reaction and backward steepness have absolutely nothing to do with the capacitance, although they also become complex at higher frequencies. These differential quantities represent exactly two controlled sources in the small-signal equivalent circuit diagram, while the capacitances are present as passive components in addition to the sources.

## literature

• F. Bergtold: Röhrenbuch for radio and amplifier technology . Weidmannsche Buchhandlung, Berlin 1936.
• Ludwig Ratheiser: The great tube manual . Franzis-Verlag, Munich 1995, ISBN 3-7723-5064-X .
• Ludwig Ratheiser: Radio tubes - properties and application . Union Deutsche Verlagsgesellschaft, Berlin 1936.