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Filtro passa basso passivo per subwoofer

Circuito del filtro passa basso Figura 1

In questo articolo è illustrato il progetto di un semplice filtro passivo del primo ordine da posizionare prima di un amplificatore collegato a un subwoofer. Il circuito, che lavora su segnali a livello di audio di linea, ha frequenza taglio regolabile tra 20 Hz e 200 Hz. Data l'assenza di componenti attivi, è estremamente semplice da realizzare, ma la frequenza di taglio dipende dall'impedenza d'uscita della sorgente audio e dall'impedenza di ingresso dell'amplificatore. In questo articolo saranno assunti dei valori tipici per tali parametri, ma si consiglia di ripetere i calcoli per ogni amplificatore. Per una soluzione più complessa ma più precisa è possibile utilizzare un Filtro passa basso attivo per subwoofer.

1 - Caratteristiche del circuito

Di seguito sono riportate le risposte in frequenza del filtro per f0 e f1, ovvero per la frequenza minima e massima di taglio del filtro. Viene inoltre presentato un grafico con la variazione della risposta in frequenza del filtro in funzione del potenziometro.

Risposta in frequenza per ft=20Hz Figura 2: Modulo della funzione di trasferimento in dB del filtro per ft = 20 Hz. In ascissa è riportata la frequenza in scala logaritmica.
Risposta in frequenza per ft=200Hz Figura 3: Modulo della funzione di trasferimento in dB del filtro per ft = 200 Hz. In ascissa è riportata la frequenza in scala logaritmica.
Frequenza di taglio in funzione del potenziometro Figura 4: Frequenza di taglio del filtro in funzione della posizione del potenziometro

1.1 - Perdite sul segnale

Come si può facilmente intuire, il circuito introduce un'attenuazione A nel segnale non filtrato al di sotto di ft, che vale: Latex: V_{OUT} = \dfrac{R_L}{R_{IN} + R_L + R_{tot}} V_{IN} Tale formula si ottiene ponendo a zero la variabile s nella funzione di trasferimento del filtro presentata nella sezione 2. Nel caso dei componenti utilizzati per questo circuito, A = 0.8. In altri termini, è una perdita di -1 dB sul segnale. E' un valore accettabile, dato che non introduce sensibili perdite.

2 - Funzionamento e progetto del circuito

La funzione di trasferimento del circuito è: Latex: H(s) = \dfrac{R_L} {C (R+ R_A)(R_L + R_{tot}- R)\cdot s + R_A + R_{tot} + R_L} e la sua frequenza di taglio: Latex: f_t = \dfrac{R_{IN} + R_{tot} + R_L} { 2 \pi C (R_{IN} + R) (R_{tot} - R + R_L)}')dove Rtot è la resistenza totale del potenziometro RP, e R è il valore assunto dal potenziometro. Per calcolare il valore dei componenti, si può scrivere un sistema composto dalla formula della frequenza di taglio valutata nei due casi limite: Latex:  
&f_t \left|_{~_{f=f_0, R=R_{tot}}} \right. ~\rightarrow~ f_0 = \dfrac{R_{IN} + R_L + R_{tot}}{2 \pi C R_L (R_{IN} + R_{tot})}  \\\\
                &f_t \left|_{~_{f=f_1, R=0}}\right. ~\rightarrow~ f_1 = \dfrac{R_{IN} + R_L + R_{tot}}{2 \pi C R_{IN} (R_L + R_{tot})}
Dove f0 = 20 Hz e f1 = 200 Hz. Risolvendo tale sistema si ottiene: Latex: 
C &= \dfrac{R^{2}_{IN} ~ f_1 - R^{2}_{L} ~ f_0}{2 \pi R_{IN} R_L f_0 f_1 (R_{IN} - R_L)} \\\\
R_{tot} &= \dfrac{R_{IN} R_L (f_0 - f_1)} {R_{IN} f_1 - R_L f_0} ')

E' ora possibile fare alcune considerazioni per determinare i valori da inserire nelle due espressioni. L'impedenza di uscita dei moderni riproduttori musicali o computer è molto piccola, pari ad alcuni Ω, e può essere quindi trascurata. L'impedenza di ingresso dell'amplificatore è invece importante. Un valore comune può essere ad esempio 20KΩ, utilizzato dal Fenice 20, un amplificatore hi-fi in classe T con potenza 15W + 15W basato sull'integrato Tripath TA2024C. Il suo valore è stato misurato con questo metodo: Misura economica dell impedenza di ingresso di un amplificatore audio. Sostituendo i valori precedenti nel sistema e scegliendo ad esempio RA = 390 Ω è possibile ottenere C = 2.2uF e RP = 4.7 KΩ.

Bibliografia e ulteriori letture

  1. Filtro passa basso attivo per subwoofer
  2. Misura economica dell impedenza di ingresso di un amplificatore audio

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Grazie, molto interessante

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