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Some devices that may be also used as amplifiers and/or oscillators have a voltage-current characteristic in ‘S’ and/or in ‘N’ that contains some portions with ‘negative slope’. Well-known examples are the tunnel diode and/or the neon tube. Those characteristics are shown in the Figure 1.
Figure 1. Current-voltage characteristics of a tunnel diode and a neon gas tube
When a signal is applied through the part of such characteristics that contains also the ‘negative slope’, a discontinuity of ‘hysteresis type’ appears (Wikipedia, hysteresis, 2012). For the tunnel diode this kind of ‘hysteresis loop’ is shown in the Figure 2.
Figure 2. Hysteresis loop for the tunnel diode
A passive component as a tunnel diode and/or a neon tube may be considered as a non-linear resistor for the whole voltage-current characteristic that does not presents a negative slope. For this last portion, the device try to act as a ‘source’ and then ‘jump’ to the nearest point with a positive slope. By rotating the axis V-I (voltage-current) of its characteristic with a convenient angle (~350 in this case) a new characteristic that presents any ‘negative slope portion’ may be obtained. For the tunnel diode, this is shown in the Figure 3. Of course, for this new characteristic, any hysteresis effect may appear.
Figure 3. I-V conveniently rotated characteristic of a tunnel diode
The rotation equations of such characteristics are (Wikipedia, rotation, 2012):
(1) where
is the rotation angle. It can be seen that a ‘physical rotation’ needs energy to be realized. For electrical signals, a simulation program and/or a hardware equivalent system may be realized to display the ‘rotated signals’. The bloc diagram of such hardware system is presented in the Figure 4.
Figure 4. Bloc diagram of a hardware system to rotate the axis of the characteristic of an electronic device presenting ‘hysteresis’
On the X-input of the rotation device, a triangular signal is applied. A sine signal having the same frequency is applied, for example, on a non-linear resistor that have a voltage-current characteristic in ‘S’ and/or in ‘N’ or on a closed loop comparator that have ‘hysteresis’. The output of this component is applied on the Y-input of the rotation device. With a dc. voltage applied on the Angle-input, the converter C will generate the necessary 
and 
voltages for the rotation. The rotated device characteristic is displayed on the Scope. Changing some components of a closed loop comparator can modify the parameters of its ‘hysteresis window’.