Name: analyzing an op amp audio filter
Uploaded: 2024-04-11T12:48:50.000Z
Duration: 1 min 18 s
Channel: JoVE

In un sistema audio, il circuito del filtro elabora il segnale audio amplificato da un amplificatore, attenuando fortemente i componenti del segnale con le basse frequenze.
Si consideri il circuito di filtro più semplice costituito da un amplificatore operazionale in configurazione invertente accoppiato con le resistenze R1 e R2 e il condensatore C1. Qual è il segnale di uscita risultante per un segnale di ingresso noto?
L'impedenza del condensatore viene calcolata utilizzando la frequenza angolare derivata dall'espressione nel dominio del tempo per la tensione di ingresso.
Il circuito equivalente nel dominio della frequenza rappresenta il segnale di ingresso in forma polare e le impedenze Z1 e Z2. L'impedenza Z2 corrisponde alla combinazione parallela del condensatore C1 e del resistore R2.
Applicando la legge corrente di Kirchoff e la legge di Ohm al nodo si ottiene un'equazione nodale per un amplificatore operazionale ideale. Questa equazione, una volta riorganizzata, indica che il rapporto tra l'uscita e la tensione di ingresso è uguale al rapporto negativo delle impedenze.
Sostituendo i valori noti e calcolati in questa equazione, la tensione di uscita viene determinata in forma polare, che viene poi convertita nel dominio del tempo.

circuiti ca con amplificatori operazionali

All'interno di un sistema audio, il circuito del filtro svolge un ruolo fondamentale nell'elaborazione del segnale audio potenziato da un amplificatore. La sua funzione principale è attenuare in modo significativo i componenti del segnale con frequenze più basse, modellando così l'uscita audio. Vengono esaminate le operazioni di questo circuito, concentrandosi sulla configurazione fondamentale del filtro. Questa configurazione prevede un amplificatore operazionale disposto in una configurazione invertente accoppiato con resistori (R1 e R2) e un condensatore (C1).

<img alt="Figure1" src="/files/ftp_upload/15116/15116_PT_Figure_1.svg" style="text-align: center; height: 164px;">

Di fronte a un segnale di ingresso noto, la sfida sta nel determinare il segnale di uscita risultante. Il primo passo prevede il calcolo dell'impedenza del condensatore, che si ottiene utilizzando la frequenza angolare, derivata dall'espressione nel dominio del tempo della tensione di ingresso.

<img alt="Equation1" src="/files/ftp_upload/15116/15116_PT_Equation_1.svg" style="text-align: center; height: 36px;">

Di conseguenza, l'analisi passa al dominio della frequenza, dove il segnale di ingresso è rappresentato in forma polare accanto ai componenti di impedenza Z1 e Z2. Z2 si riferisce esplicitamente alla combinazione parallela del condensatore C1 e del resistore R2. Il nucleo dell'analisi si basa sull'applicazione della legge della corrente di Kirchhoff e della legge di Ohm a un nodo specifico del circuito, formulando così un'equazione nodale per un amplificatore operazionale ideale. Questa equazione, una volta riorganizzata, rivela un'intuizione fondamentale: il rapporto tra la tensione di uscita e quella di ingresso è inversamente proporzionale al rapporto delle impedenze.

<img alt="Equation2" src="/files/ftp_upload/15116/15116_PT_Equation_2.svg" style="text-align: center; height: 36px;">

I valori noti e calcolati, vengono abilmente sostituiti in questa equazione per svelare la tensione di uscita in forma polare. Il risultato, che rappresenta la tensione di uscita, può quindi essere trasformato nel dominio del tempo, fornendo una comprensione completa della risposta del circuito di filtro al segnale di ingresso. Per l'analisi, si presuppongono spesso le proprietà ideali dell'amplificatore operazionale, incluso il principio secondo cui nessuna corrente entra in nessuno dei suoi terminali di ingresso e che la tensione ai suoi terminali di ingresso rimane zero.

Circuiti CA con Amplificatori Operazionali

In un sistema audio, il circuito del filtro elabora il segnale audio amplificato da un amplificatore, attenuando fortemente i componenti del segnale con ...

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JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

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AC Circuit Analysis

Analisi dei circuiti in CA

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Op Amp AC Circuits

analyzing an op amp audio filter

An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1.

The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the time-domain form of the input voltage, so the work moves into the frequency domain.

In the frequency domain, the input signal is written in polar form. The impedances Z1 and Z2 are then used, with Z2 representing the parallel combination of capacitor C1 and resistor R2. At the same time, the ideal op amp assumptions are used. No current enters either input terminal, and the voltage across the input terminals is zero.

The final step is applying Kirchhoff's current law and Ohm's law at one node in the circuit. This creates a nodal equation for the ideal op amp. When that equation is rearranged, the output-to-input voltage ratio is shown to be inversely proportional to the impedance ratio. The known values are then substituted to find the output voltage in polar form, and that result can be converted back to the time domain for a full description of the filter response.

Analyzing an Op Amp Audio Filter

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An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1. The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the...

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Learn how an op amp audio filter reduces low-frequency signals. Follow impedance, nodal analysis, and polar-to-time-domain output calculations.

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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

Analyzing an Op Amp Audio Filter

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