Re: CNET: Audiophile grade computer speakers for $199On Sat, 31 May 2008 20:12:53 -0700, dpierce.cartchunk.org@gmail,com wrote
(in article <g1t43l02mld@news4.newsguy,com >):
> On May 31, 11:30 am, Sonnova <sonn...@audiosanatorium,com > wrote:
>> On Fri, 30 May 2008 07:50:09 -0700, dpierce.cartchunk....@gmail,com wrote
>> (in article <g1p4710...@news3.newsguy,com >):
>>
>>
>>
>>> On May 29, 10:56 am, Sonnova <sonn...@audiosanatorium,com > wrote:
>>>> On Wed, 28 May 2008 07:49:55 -0700, Dave wrote
>>>> (in article <g1jrej0...@news2.newsguy,com >):
>>
>>>>> "Arny Krueger" <ar...@hotpop,com > wrote in message
>>>>> news:g14s5n02inn@news1.newsguy,com ...
>>>>>> I thought that the AudioEngine 2 review begged comparison with this one
>>>>>> for
>>>>>> the classic NHT SZ:
>>
>>>>>> http :// www .stereophile,com /loudspeakerreviews/804/index9.html
>>
>>>>> I am curious about the high-pass filter employed in the article. The
>>>>> author
>>>>> notes that the R in the RC filter is in parallel with the amplifier's
>>>>> output
>>>>> impedance of 51K. Given that the amp's impedance is upstream of the
>>>>> capacitor, is this right? Or did he actually construct a filter with a
>>>>> rolloff frequency of 106Hz?
>>
>>>>> Vin Vout
>>>>> o------------||-----------------o
>>>>>> 0.1uF "C" of |
>>>>> \ RC filter \
>>>>> / /
>>>>> 51K \ Amp \ 15K "R" of RC filter
>>>>> / /
>>
>>>>> o-------------------------------o
>>
>>>> That's a classic single-pole high-pass filter "Pi" network. But such a
>>>> filter
>>>> is only 3dB/octave - not very steep.
>>
>>> Explain, if you will, how a single-pole filter has
>>> a slope of 3 dB/octave.
>>
>> I'm reasonably sure that a single-pole passive high-pass
>> filter is 3dB down at half it's corner frequency and rolls
>> off at a rate of 20dB/decade.
>
> Fine, let's assume that's true. How many octaves
> are there per decade? Well, there are about 3 1/3
> (since 2^3.33 ~= 10). Thus
>
> 20 dB/decade / 3.33 octaves/decade=
>
> Hmmm, 6 dB per octave, not 3 dB/octave.
>
> Thus, your own assertion demonstrates that
> a single pole filter has a slope of 6 dB/octave
> in the stop band.
>
>> The response chart at :
>>
>> http :// tinyurl,com /5k4tzo
>>
>> Shows the slope. If you interpolate the graph,
>> you can see that the shown 10KHz high-pass
>> is down by about that much at 5KHz
>
> No, it shows the slope asymtotically approaching
> 6 dB/octave. Look, for example, at the difference
> between 1 kHz and 500 Hz, 200 Hz and 100 Hz,
> and so on. All 6 dB/octave for single pole.
>
> The roloff rate is NOT taken at cutoff, it's taken
> in the stop band and is the ultimate roloff rate.
>
> Constructing a 3dB/octave filter with that slope
> over a wide bandwidth is not a trivial excercise,
> because it implies a "half-pole" filter, somethinfg
> that's mathematical nonsense. Instead, ther are
> constructed using a series of poles and zeros
> staggered evenly in frequency so they do a piece-
> wise approximation of a 3 dB/octave slope. But,
> in this case, it's a multi-pole filter that has the
> (approximate) 3 dB/octave slope.
>
> Bottom line: all of your data confirms that the
> rolloff rate of the single pole filters we're talking
> about is 6 dB/octave.
OK. I mis-remembered.