6.15
Circuits CA d'amplificateur opérationnel
Au sein d'un système audio, le circuit de filtrage joue un rôle central dans le traitement du signal audio amplifié provenant d'un amplificateur. Sa f…
Dans un système audio, le circuit de filtrage traite le signal audio amplifié d’un amplificateur, atténuant fortement les composantes du signal à basse fréquence.
Considérons le circuit de filtrage le plus simple composé d’un amplificateur opérationnel dans une configuration inverseuse couplée aux résistances R1 et R2 et au condensateur C1. Quel est le signal de sortie résultant d’un signal d’entrée connu ?
L'impédance du condensateur est calculée à l'aide de la fréquence angulaire dérivée de l'expression dans le domaine temporel de la tension d'entrée.
Le circuit équivalent dans le domaine fréquentiel représente le signal d’entrée sous forme polaire et les impédances Z1 et Z2. L’impédance Z2 correspond à la combinaison parallèle du condensateur C1 et de la résistance R2.
L'application de la loi du courant de Kirchoff et de la loi d'Ohm au nœud donne une équation nodale pour un ampli-op idéal. Cette équation, lorsqu’elle est réarrangée, indique que le rapport entre la tension de sortie et la tension d’entrée est égal au rapport négatif des impédances.
En substituant les valeurs connues et calculées dans cette équation, la tension de sortie est déterminée sous forme polaire, qui est ensuite convertie dans le domaine temporel.
View the full transcript and gain access to JoVE Core videos
Q1: How does an inverting op-amp filter circuit attenuate low-frequency audio signals?
An inverting op-amp filter uses resistors R1 and R2 coupled with capacitor C1 to process amplified audio signals. The capacitor's impedance varies with frequency, causing the circuit to strongly attenuate low-frequency components while allowing higher frequencies to pass. This frequency-dependent behavior shapes the audio output by reducing unwanted bass frequencies.
Q2: What role does capacitor impedance play in frequency domain analysis of op-amp filters?
Capacitor impedance is calculated using angular frequency derived from the input voltage's time-domain expression. In the frequency domain, this impedance combines with R2 to form impedance Z2. The frequency-dependent impedance determines how the circuit responds to different signal frequencies, enabling the analysis to predict output voltage behavior across the audio spectrum.
Q3: How is the output voltage determined in an inverting op-amp filter circuit?
Applying Kirchhoff's current law and Ohm's law at the op-amp node yields a nodal equation. When rearranged, this equation shows that the output-to-input voltage ratio equals the negative ratio of impedances Z1 and Z2. Substituting known values into this relationship produces the output voltage in polar form, which converts to the time domain for practical interpretation.
Q4: Why is the input signal represented in polar form during frequency domain analysis?
Polar form representation simplifies AC circuit analysis by expressing sinusoidal signals as magnitude and phase components. This format aligns with impedance calculations and enables straightforward application of circuit laws using phasors. Converting between time domain and polar form allows engineers to analyze filter behavior systematically and predict output characteristics.
Q5: What assumptions about ideal op-amps are essential for filter circuit analysis?
Ideal op-amp analysis assumes no current enters either input terminal and the voltage across input terminals remains zero. These assumptions simplify nodal equations and enable direct application of Kirchhoff's laws without accounting for input impedance effects. This idealization makes the mathematical analysis tractable while remaining accurate for practical high-gain operational amplifiers.
Q6: How does impedance combination affect the filter circuit's frequency response?
The parallel combination of capacitor C1 and resistor R2 creates impedance Z2, which varies with frequency. As frequency increases, capacitive reactance decreases, changing the impedance ratio and thus the voltage gain. This impedance combination directly determines which frequencies are attenuated and which pass through, shaping the filter's overall frequency response characteristic.
Q7: What is the significance of converting output voltage from polar form back to time domain?
Converting from polar form to time domain transforms the mathematical solution into a practical sinusoidal expression that describes actual circuit behavior over time. This conversion reveals the output signal's amplitude and phase shift relative to the input, providing engineers with actionable information about how the filter modifies the audio signal in real-world applications.