Name: first-order circuits in flashing lamps
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 15 s
Channel: JoVE

Elektrische Schaltungen mit Widerständen und einem einzigen Energiespeicherelement - einem Kondensator oder einer Induktivität - werden als Schaltungen erster Ordnung bezeichnet.
Sie werden durch eine Differentialgleichung erster Ordnung beschrieben, die Eingangs- und Ausgangssignale in Beziehung setzt.
RC-Schaltungen werden in Relaxationsoszillatoren wie Neonlampen-Oszillatorschaltungen verwendet.
Wenn eine Spannung angelegt wird, beginnt der Kondensator zu laden, und die Lampe fungiert als offener Stromkreis. Wenn der Kondensator die erforderliche Spannung erreicht, um das Neongas zu ionisieren, wird die Lampe zu einem Kurzschluss.
Der Kondensator entlädt sich, wodurch ein Blitz entsteht, und der Vorgang wiederholt sich.
Das Zeitintervall zwischen den Blitzen hängt von der Zeitkonstante ab, die durch Einstellen der R- und C-Werte einstellbar ist.
In Röhrenleuchten wird eine RL-Schaltung verwendet, bei der eine Drossel als Induktivität und der inhärente Drahtwiderstand als Widerstand fungieren.
Beim Anlegen der Spannung widersteht die Drossel plötzlichen Stromanstiegen und erzeugt eine EMK, die mit der angelegten Spannung zunimmt. Diese EMK ionisiert das Gas und beleuchtet das Röhrenlicht.
In einer RL-Schaltung ist die Induktivität über dem Widerstand die Zeitkonstante.

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schaltkreise erster ordnung

First-Order Circuits

Elektrische Schaltkreise erster Ordnung, die aus Widerständen und einem einzelnen Energiespeicherelement – entweder einem Kondensator oder einer Induktivität – bestehen, sind für viele elektronische Systeme von grundlegender Bedeutung. Diese Schaltkreise unterliegen einer Differentialgleichung erster Ordnung, die die Beziehung zwischen Eingangs- und Ausgangssignalen beschreibt. Ein gängiges Beispiel für eine Schaltung erster Ordnung ist die RC-Schaltung (Widerstand-Kondensator). Diese Schaltungen werden in Relaxationsoszillatoren wie Neonlampen-Oszillatorschaltungen verwendet. Wenn Spannung an einen RC-Kreis angelegt wird, beginnt der Kondensator aufzuladen und die Lampe fungiert als offener Stromkreis. Wenn sich der Kondensator auf die erforderliche Spannung auflädt, um das Neongas in der Lampe zu ionisieren, entsteht in der Lampe plötzlich ein Kurzschluss. Dadurch entlädt sich der Kondensator und es entsteht ein Lichtblitz. Sobald der Kondensator vollständig entladen ist, wiederholt sich der Vorgang und führt zu einem kontinuierlichen Blinkeffekt. Das Zeitintervall zwischen diesen Blitzen hängt von der Zeitkonstante des Stromkreises ab, die durch Anpassen der Widerstands- (R) und Kapazitätswerte (C) angepasst werden kann. Durch sorgfältige Auswahl dieser Werte kann die Häufigkeit der Blitze gesteuert werden. In Röhrenleuchten wird eine andere Art von Schaltung erster Ordnung verwendet, die als RL-Schaltung (Widerstand-Induktivität) bekannt ist. Die Drosselspule in der Röhrenleuchte dient als Induktor, während der Eigenwiderstand des Drahtes als Widerstand fungiert. Beim Anlegen einer Spannung widersteht die Drossel einem plötzlichen Stromanstieg und erzeugt eine elektromotorische Kraft (EMK), die mit der angelegten Spannung ansteigt. Diese EMK ionisiert das Gas in der Röhrenleuchte und bringt sie zum Leuchten. In einer RL-Schaltung ist die Zeitkonstante als Induktivität (L) über dem Widerstand (R) definiert. Diese Zeitkonstante spielt eine entscheidende Rolle bei der Bestimmung, wie schnell die Schaltung auf Änderungen im Eingangssignal reagiert. Je größer die Zeitkonstante, desto langsamer reagiert die Schaltung und umgekehrt.

Schaltkreise erster Ordnung

Elektrische Schaltungen mit Widerständen und einem einzigen Energiespeicherelement - einem Kondensator oder einer Induktivität - werden als Schaltungen erster Ordnung bezeichnet.
Sie werden durch eine ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

First and Second-Order Circuits

Schaltungen erster und zweiter Ordnung

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

first-order circuits in flashing lamps

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals.

One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor reaches the voltage needed to ionize the neon gas, the lamp suddenly acts like a short circuit.

That change lets the capacitor discharge, and the lamp flashes. After the capacitor fully discharges, the same cycle begins again. This repeated charge-and-discharge process creates a steady flashing effect. The time between flashes depends on the circuit time constant, which can be adjusted by changing the resistance R and capacitance C. By selecting different values, the flash frequency can be controlled.

Tube lights use another first-order circuit called an RL circuit, which contains a resistor and an inductor. In this case, the choke coil works as the inductor, and the wire resistance acts as the resistor. When voltage is applied, the choke resists a sudden rise in current and produces an electromotive force, or emf, that grows with the applied voltage. This emf helps ionize the gas in the tube light, so the lamp turns on.

For an RL circuit, the time constant is L divided by R, where L is inductance and R is resistance. This value shows how quickly the circuit responds to changes in the input signal. A larger time constant means a slower response, while a smaller one means a faster response.

First-Order Circuits in Flashing Lamps

first-order circuits

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals. One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor...

rc circuit without source

RC Capacitor Discharge After Power Loss

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit. Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in...

rc circuit with source

RC Circuit Charging After a DC Step

An RC circuit with a DC source shows how a capacitor charges after a sudden voltage step. The applied source is treated as a unit step function, and the capacitor voltage is the step response of the circuit. This response describes how the circuit reacts right after the input changes. A capacitor cannot change its voltage instantly. So, immediately after the switch closes at t=0, the capacitor voltage stays at its initial value. Kirchhoff’s current law is then applied at that moment and...

rl circuit without source

RL Circuit Decay After Source Removal

An RL circuit begins to decay after the DC source is removed. At that moment, the circuit becomes source-free. If the inductor has an initial current, I0, it also stores initial energy. That stored energy drives the natural response of the circuit. Kirchhoff’s voltage law is applied around the loop. The inductor voltage and resistor voltage are substituted into the equation. This gives a first-order differential equation for the current. Rearranging the terms produces a logarithmic form, which...

rl circuit with source

RL Step Response Under a DC Source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied. During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source...

design example: frog muscle response

RL Circuit and Frog Leg Current Response

An RL circuit is used to model the frog leg’s response to electrical stimulation. In this setup, the student studies how current changes in a resistor-inductor circuit can trigger muscle contraction. The circuit provides a way to control and measure the electrical impulses involved in the experiment. When the switch is closed, the frog’s leg shows a brief contraction. At steady state, the inductor acts like a short circuit. That lets current bypass the resistor and produces a mild, short...

second-order circuits

RLC Damping and Resonant Frequency

Second-order circuits use two energy storage elements, such as a capacitor and an inductor, to shape how current and voltage change over time. These circuits include RLC circuits, along with RC and RL circuits that have two capacitors or two inductors. Their behavior is described by second-order differential equations that connect the input signal to the output signal. The input usually comes from a voltage source or a current source. The output is often the voltage across the capacitor, the...

series rlc circuit without source

Natural Response of a Source-Free RLC Circuit

A source-free RLC circuit is a series circuit with a resistor, inductor, and capacitor, but no external energy source. It begins with the energy already stored in the capacitor and inductor. That stored energy drives the circuit at first. The circuit is described by a second-order differential equation. This equation shows how the resistor, inductor, and capacitor interact over time. The resistor removes energy from the circuit, so the solution has an exponential form. When the exponential...

types of responses of series rlc circuits

types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

A source-free series RLC circuit shows three response patterns based on damping. The circuit is described by a second-order differential equation. Its complete solution is made from two distinct solutions. Those solutions depend on the roots, which are written in terms of the damping factor and the resonant frequency. When the damping factor is greater than the resonant frequency, both roots are real and negative. This gives an overdamped response. The circuit output decays slowly over time. <br...

series rlc circuit with source

Forced Response in a Series RLC Circuit

A series RLC circuit with a DC source can model an automobile ignition system. The circuit shows how a battery can produce the high voltage needed for a spark. In this case, the input DC voltage acts like a forcing step function. Applying Kirchhoff's voltage law leads to a second-order differential equation. A second-order differential equation is an equation with a term for the second derivative. The form of this equation is very similar to the one used for a source-free RLC circuit, so the...

parallel rlc circuits

Parallel RLC Step Response in Surge Protectors

Parallel RLC circuits help explain how a surge protector works in a street lamp. The circuit model uses a DC input source that creates a step response when the switch is turned on. This setup shows how the lamp’s components can be protected from sudden voltage spikes. When the switch closes, Kirchhoff’s current law is applied to the parallel RLC circuit. That leads to a second-order differential equation. The solution has two parts: a transient response and a steady-state response. The...

second-order op amp circuits

Second-Order Op Amp Low-Pass Filters

Second-order op-amp low-pass filters remove unwanted high-frequency noise from audio signals. They are used in audio systems to refine sound quality. These filters are often built as voltage followers and have two nodes with storage elements. The circuit analysis follows the same basic method used for second-order RLC circuits. In practice, bulky inductors are usually avoided because of their size and weight. For that reason, the focus here is on RC second-order op-amp circuits, which are...

design example: underdamped parallel rlc circuit

design-example-underdamped-parallel-rlc-circuit

Oscillator Design with a Parallel RLC Circuit

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design. The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance...

key terms and concepts

Explore RC and RL first-order circuits through neon lamps and tube lights. Learn how time constant, resistance, capacitance, and inductance control circuit response.

First-Order Circuits in Flashing Lamps | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

First-Order Circuits in Flashing Lamps

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