Please help with theoretical 6db crossover question

[norman bates]

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

 

[stevebogus]

No, in your example the tweeter is not 6dB down at the crossover frequency. It is down 3dB.

 

[rayma]

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?

 

[norman bates]

feisty, thanks for asking............

 

[GM]

T = R / (R + 1/jwC)........

Sheesh! Thanks, never seen the math; now I know why my mentor just said odd orders = -3 dB, even orders = -6 dB.

GM

 

[rayma]

Sheesh! Thanks, never seen the math; now I know why my mentor just said
odd orders = -3 dB, even orders = -6 dB.

It's good to understand the EE101 fundamentals, and not just use a simulator.

 

[turk 182]

i guess i'm too much of a Hitchcock fan to ever ask a guy with that name about his mom...


if the assumption of a "nice flat 8 ohm load" where true wouldn't that result in a stepped response?

 

[rayma]

if the assumption of a "nice flat 8 ohm load" where true wouldn't that result in a stepped response?

That would give the ideal first order crossover curve.
Higher order filters can give a sharper corner, but none can be square.

 

[chris661]

Sheesh! Thanks, never seen the math; now I know why my mentor just said odd orders = -3 dB, even orders = -6 dB.

GM

Kind-of.

Even order tend to be Linkwitz-Riley slopes, which are indeed 6dB down at the crossover point.
Odd order tend to be Butterworth, -3dB at the crossover point.

LR crossovers sum flat on-axis.

Chris