Please help with theoretical 6db crossover question

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Let’s take a cap on a tweet.
Let’s assume a nice flat 8ohm load………….. (lol)
The formula C = 1 / ( 2 x Pi x F x R)

So, given 8ohm tweet, 5khz, the value is about 4uF

My question is “Is it 6db down at that frequency” ?


I'm hoping to ghost a tweet in.........................


Norman
 
T = R / (R + 1/jwC) normalized HP filter, with corner = ( 2Pi x f ) = w = 1/RC

T = jwRC / (jwRC + 1)

| T | = sqrt ( T x T* )

| T | = sqrt [ [ jwRC / (jwRC + 1) ] x [ -jwRC / (-jwRC + 1) ] ]

| T | = sqrt [ (wRC)^2 / ( 1 + (wRC)^2 ) ]

at the corner frequency, w = 1/RC

| T | = sqrt [ 1 / 2 ]

| T | = 1 / sqrt 2 = 0.7071

20 x log ( 0.7071 ) = 20 x (-0.15052) = -3.01 dB at w = 1/RC or f = 1 / (2Pi x RC)

How's your mom?
 
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