Exploring Stability and Resonance in Unstable Circuits with Right-Side Poles

In summary, a circuit with poles in the right-hand side of the imaginary-real plane (unstable system) can have a resonant frequency if it is an active circuit. In theory, this circuit will produce oscillations with a growing amplitude, but in a real circuit, non-linearities will cause the amplitude to remain fixed. The output will have a fundamental frequency of the resonant frequency.
  • #1
EvLer
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Can a circuit that has transfer function with poles in right-hand side part of the imaginary-real plane (unstable system) have resonant frequency?
 
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  • #2
EvLer said:
Can a circuit that has transfer function with poles in right-hand side part of the imaginary-real plane (unstable system) have resonant frequency?
Sure. Several of my circuit designs had a resonant frequency that they kept wanting to find... :-)
 
  • #3
EvLer said:
Can a circuit that has transfer function with poles in right-hand side part of the imaginary-real plane (unstable system) have resonant frequency?
No passive circuit can have poles in the RHP. An active circuit can have them and the output (assuming second order behavior) will be:
[tex]ke^{\alpha t}cos(\omega_g t + \phi)[/tex], where [tex] \omega_g[\tex] is the resonant frequency.
Theoretically this circuit will produce oscillations in the frequency [tex] \omega_g[\tex] with amplitude growing to infinity.
In a real circuit, when the amplitude grows, non linearities arise and the circuit will oscillate with fixed amplitude. Only we would not have a sinusoid anymore, but a distorted waveform, whose fundamental frequency is [tex] \omega_g[\tex] .

I don´t understand why LaTex has not generated the correct image.
 
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Related to Exploring Stability and Resonance in Unstable Circuits with Right-Side Poles

1. What is stability and why is it important in science?

Stability refers to the ability of a system to maintain its equilibrium or constant state. In science, it is important because it allows us to predict and understand how a system will behave over time.

2. How is stability related to resonance?

Resonance is a phenomenon where a system is driven to oscillate at a specific frequency. Stability and resonance are related because a system that is stable will have a natural frequency of oscillation, and if this frequency matches the driving frequency, resonance can occur.

3. What are the factors that affect stability and resonance?

The factors that affect stability and resonance include the properties of the system, such as its mass, stiffness, and damping, as well as the external forces acting on the system.

4. How does the concept of stability and resonance apply to real-life situations?

Stability and resonance can be seen in various real-life situations, such as the swinging of a pendulum, the vibrations of a guitar string, and the movement of a bridge in response to wind or traffic.

5. Can stability and resonance be controlled or manipulated?

Yes, stability and resonance can be controlled and manipulated by changing the properties of the system or by applying external forces. For example, engineers can design structures to have specific natural frequencies to avoid resonance, and musicians can change the tension of guitar strings to change their frequency of oscillation.

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