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Amp math (long)

>From: "Stephen D. Cohen" <cohensd@domain.elided>
>Date: Fri, 30 Aug 1996 22:53:08 -0400
>Subject: Re: Dings, M3 Interest Group Newsletter, M3 Stereo Update
>
...
>
>3. '95 M3 Stereo Update
>
>Thanks to all who responded to my tale of woe. Responses were "it
>sucks", "rip it out", and so on. BMWNA Factory Rep looked at it...note
>- he didn't bother listening to it - and said it is the ONLY system
>BMW put into '95 M3 [remember 250 watts identification is TOTAL
>crap...defined by BMW to me as "peak power at peak distortion" - they
>later in early '95 called it 200 watt system - peak power at 10% THD -
>plus it 20 watts into 10 channels. Basically...BMW is saying - it is
>what it is. Sucko and Vanzatti for such a fabulous performance car.
>
>To cut to the chase what I did is as follows:
>
>Sony ES CDX-X810DSP [head unit] - cd receiver (in-dash) with built-in
>amp at 35 watts RMS power at 1% THD into 4 channels, digital signal
>processor, etc. Sony ES CDX-91 - 10 cd changer (in trunk). MB Quart
>Soundset up front - Model QM 325.21 - 3-way speaker system designed
>for BMW E36 2-door model, including: 5.25" woofer, 4" midrange with
>coaxially mounted .75" titanium tweeter. Left rear speakers alone for
>now. Installed cost approx. $1800.
>

Hmmm, lets see what the specifications say: Sony CDX-C810DSP, 14 W x 
4 into 4 ohms with 1 % THD. The 35 W is again some marketing hype...

Since lots of people here seem to be lost with amps and power ratings 
lets do some amp math... Car amps, either inside a head unit or 
separate, can be divided into 3 groups. How amps work (A, B etc. 
classes) is another issue...

1. The least powerful amps use a single amplifier. Due to the fact 
that a car battery voltage is only 12 V .. 15 V (while charging), and 
an amp has to create AC output to move the speaker cone in and out, 
an amp has only half of the supply voltage to use. Of that voltage 
1 .. 2 V is lost because of component properties. You get out 
something like 6 V PEAK voltage. To a 4 ohms load it means 9 W PEAK 
power. If the signal is simple sine wave, eg. a single 1 kHz 
frequency, the RMS voltage is peak voltage/1.41. RMS power would be 
4.5 W to 4 ohms. Then there is distortion. Close to clipping level 
amplifiers are not linear. With good design an amp like this could 
give out 4 W to 4 ohms with 1 % THD.

2. Bridged amplifiers with no switching power supply. These are 
simply two amplifiers connected so that they each make their own half 
of the output voltage. They can use the whole supply voltage range 
minus the losses. In theory the output voltage is  x2 and power x4 
compared to group 1 amps. The drawback is worse linearity resulting 
in more distortion. In theory peak power could be 12 V^2/4 ohms = 
whopping 36 W (pretty close to 35, isn't it). Rms power could be (12 
V/1.41)^2/4 ohms = 18 W. In practice a good design results something 
like 14 W per channel with a reasonable level of THD.

3. Amplifiers using a switching power supply. These can be bridged or 
not bridged. The power supply breaks, switches the battery voltage 
to convert it to AC. The AC voltage is then put through a transformer 
that converts it to higher voltage. The higher AC voltage is 
rectified and filtered to make a higher DC voltage. The output power 
can be almost anything and is not limited by the battery voltage. 
These amps can internally use eg. +/- 40 supply voltage to the output 
stage.

Watch for words PEAK, RMS, THD and how many channels there are in 
manufacturers power readings. A good example is the BMW amp. 200 W is 
20 W x 10 channels. Even the 20 W is quite high for an amp like this.

Anything from 5..15 W per channel with no mention about distortion is 
most likely a group 1 amp. Expect max. 4 W to 4 ohms. Anything from 
20 W to 35 W per channel is max. 14 W to 4 ohms. With group 3 amps, 
read carefully! I would only compare amp's RMS power to same load, 
typically 4 ohms, with max 1 % THD. I have not yet seen a head unit 
that has a switching power supply for amps. There is good reason for 
that. Switching power supplies create a lot of electrical noise which 
you don't want close to sensitive circuits. Lack of space is another 
reason.

Inside the BMW 95 M3 amp are 5 Philips TDA1552Q amplifier chips. I
don't have a Philips data book but I believe these chips have two
bridged output channels. Somebody with a data book could confirm this.
Assuming I am right this results in something like 5 x 14 W x 2. So
the BMW amp has more power than the Sony head unit. What makes the
situation even better is the thing that the BMW head unit has built in
crossovers for the speakers and power is not lost in the passive
crossover circuits. In theory this sounds good but I agree that the
sound quality could be better.

I would start upgrading the system with better speakers like you did. 
The problem is that the system is so integrated that you easily end 
up changing everything while weighing the options. I started by 
replacing the head unit and adding a CD-box because the head unit 
would not work properly in Europe where I am going. Replacing the 
front speakers meant scrapping the amp, putting in new ones and so 
on. Expect to spend min. 1500 $ for such changes. But it sure sounds a 
lot better now! 

Hope this helps,

Jari