L-Pads, Potentiometers and Resistors
variable resistor - potentiometer, variable resistor, rheostat, pot.
Assume a mid-range unit of 12 to 15 ohms to be used in a 2 way system. One particular model in my possession has an free air impedance of 12.8 ohms at 1000 hz. This would require a capacitor of 12.44 uF in a first order filter. The speaker used here is a 5" Wharfedale with the red square magnet used in early Wharfedale systems pre-dating the early 60's.
Now we add a parallel variable resistor (potentiometer) of 50 ohms to attenuate the high pass section. With the potentiometer (pot) fully clockwise, there is no serious problem as the 50 ohms is bypassed. However, that 50 ohms is now in parallel with the 12.8 ohms of the speaker, giving a load impedance of 10.19 ohms. This will cause the crossover frequency to shift to 1256 hz using the same 12.44 uF capacitor. If compensation were made for the 50 ohms, a capacitor of 15.63 uF would have been required for a crossover point of 1000 hz.
I doubt that Mr. Briggs made this compensation as the early units, such as the W3 which has a 12 uF capacitor and a 1000 hz crossover at the lower end of the mid-range pass-band.
As As the pot is turned CCW (counter clockwise) to attenuate the speaker, the filter freaks out. The table below shows the change of impedance and crossover frequency as the pot is turned counter clockwise to 2 o'clock, noon and 10 o'clock.
WIPER fc hz Z ohm
full CW 1256 10.19
2 o'clock 510 25.14
noon 364 35.14
10 o'clock 284 45.14
As the impedance rises, the crossover frequency drops. One would think the smaller mid-range/tweeter would be in danger at such low frequencies but this is not the case when one analyses the power transfer.
Let's assume 4V rms being applied to the ssystem. With no pot, this would be 1.25Wrms. Considering that most high frequencies reproducers will produce at least 92 dB 1W1M in their pass-band, 1.25 watts into such a driver will produce more precisely 92.22 dB, which is quite loud, especially above 1000 hz where the ears are most sensitive.
Now, lets see what happens when the pot is turned to mid-point, noon. We've added 25 ohms in series and 25 ohms in parallel with the tweeter. The circuit now will dissipate only 0.455 watts, 0.324 being dissipated by the 25 ohms series resistor and a paltry 0.131 watts by the tweeter and parallel resistor. This is assuming the same 4 Vrms applied. That would be an attenuation of 8.8 dB in the speaker's pass-band.
I don't know of any tweeter that couldn't handle 0.131 watts at 364 hz.
Many crossovers have been designed in this manner, using either a fixed resistor or an L-pad in line with the tweeter and also mid-range in a 3 way system. Unbeknownst to them is the crossover frequency shift after inserting the resistor or pad. While the L-pad will have much less effect on the load impedance than a fixed resistor, the effect on the impedance of their insertion should be considered when calculating the crossover components. This is especially true for second and third order filters used by those who want a more precision crossover in so-called high-end systems.
The use of a fixed resistor to attenuate a mid-range and/or tweeter is the better choice if that added resistance is accounted for in the crossover design when calculating the component values. Variable resistors and/or L-lads will eventually become flaky not to mention the crossover frequency shift when their position is changed if installed after the crossover is designed.
There are other pad configurations, such as the T-pad, H-pad and the p-pad.
|Impedance curves of
the Wharfedale W5 five inch unit. The red trace is that of the W5
in free air, which is not only the typical method of measurement but
also it's mode of operation. (modus operandi)
The blue and green traces are those after the addition of the 50 ohm parallel rheostat with positions of 5 o'clock and high noon, resp.
The purple trace at the top is with the rheostat fully counter-clockwise, at 7 o'clock. In this position, the speaker is shorted (bypassed) and all the filter sees is the 50 ohms resistor which is actually 47 ohms).
Admittedly, turning the tweeter or mid-range down gives the manufacturer an opportunity to please the customer who really doesn't care about crossover frequency shift as long as the system sounds good. D.I.Y.ers may have a different point of view.
The lower half of this schematic might need clarification. The voltages across each half of the 50 ohms pot, R1A and R1B were measured, hence the (M). The current through the two series resistors as marked to their right may be misleading, they are calculated but keep in mind that R1B is in parallel with the speaker's voice coil. What we have is a 9.293 ohms in series with 25 ohms.
The whole point of this was to determine whether a 15W rheostat was necessary as suggested by some members of various audio fora. Wharfedale used 3W rheostats and is appears that this power rating is more than adequate.
The speaker's phase shift is noted below at various frequencies although this correction was not applied to the power figures shown. The deviation is of the order of a few percent.
The 1.3v across S1 is rounded from 1.26v; the latter is correct considering an 18 degree phase shift. This also applies to the 1.3v which was rounded from 1.33v. The phase shift across the speaker is 18 degrees @ 3khz, the cosine of which is 0.9511. When 1.33 is multiplied by 0.9511, we get 1.2649v.
The meters I use, Fluke and Tektronix can resolve to 0.0001vac, 1/10th of a millivolt. The Tektronix is an AA501 distortion analyser with a voltmeter accuracy of 2% between 20hz & 20khz and 4% between 10hz & 100 khz.
The Flukes have an accuracy of 1% between 20hz & 20khz with an input of up to 200vac. These Flukes are also used to measure current and have an accuracy of 1% between 45hz & 10khz. Between 20hz & 45hz and 10khz and 20khz, their accuracy is 2%
Note: The word "fora" is an older plural of forum (Latin).
Another non-pertinent piece of info is that the plural of "opus" is "opera". So, I guess an opera is a collection of opera. (opuses).
Just a couple of piccies showing the test setup and equipment
The amplifier is a late 1950's EICO HF-30, a 30W mono amp of which I have two, one converted to 15W single ended
along with an EICO HF-61 preamp, all restored and in use on a 1956 design by Wharfedale.
These pages go back to 2006
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