f3 of passive radiator-system

[MCPete]

My P.R. system has two 8 inch woofers and was aligned according to Table 3.1 on p.68 of the fifth edition of the Loudspeaker Design Cookbook by Dickason. Qts = 0.45.

Measured f3 is about 40% higher than the predicted value according to the table, so I'm wondering what mistake I'm making.

In measuring f3, I'm applying only 500 mV to the driver, so I doubt that the unconnected woofer acting as a P.R. is providing less excursion than needed.

Qts of the driven woofer, volume of the box and box resonance frequency have been checked and double checked- as far as I can tell, everything is aligned as it is supposed to be.

The unconnected woofer acting as P.R. has an additional 25 grams (5 nickels) attached to its cone.

Any thoughts about what is wrong? Table 3.1 is attributed to Small and Dickason says that the table assumes delta = alpha, that is, the passive radiator has the same cone, suspension and basket as the driver, which is what I'm doing.

-Pete

[Ron E]

Have you modeled it using software? "Woofer PR's" often have a rather high PR notch, resulting in rapid rolloff and less than expected extension. Also suspect is your measurement of F3, which can be deceptively difficult. Other things that reduce bass response - mistuning, box leaks, excessive stuffing - especially when too near driver or PR, and PR Q that is too low....what is Qms of woofer? How much mass did you add?

Post the parameters...someone will model it.

[ocool_15]

Did you use the manufacturer specs or did you measure the driver yourself?
Are you trying to measure this through an impedence sweep or with a mic?

[roddyama]

To add to Ron's statement about your measurements, unless you have an anechoic room you will need to use close mic methods to make your measurements. This means, as in ported systems, the drivers output and the PR's output are measured separately and summed for total response. Be sure you know the FR of the measuring equipment so you can compensate for them as well.

[MCPete]

Unfortunately I don't have modeling software for P.R.-systems, but would be happy to find out what is available.

Normal Qms of the woofer (see below) as measured by me equals 2.89. According to the spec sheet, Qms = 4.24.

Mass added to the P.R. is 25 grams.

I doubt that the box is leaky as I was careful about caulking all joints. There is zero stuffing in the box.

My method of measuring f3 might not be the most accurate in the world. The set-up is two amplified electret condenser mikes, one nearfield to each of the two woofers. Electrically summing the outputs of the two mikes gives the output voltage level directly proportional to SPL of the speaker system. To measure f3, I read the output voltage at 200 Hz, multiply that figure by 0.71 and find the frequency at which the output voltage equals that product. While making these measurements, I'm checking that input voltage to the driver is constant at 500mV.

The woofers are DVC and the driven woofer has one of the voice coils shorted with the following measured parameters:

Re: 6 ohm
Fs: 46 Hz
Qts: 0.45 Hz
Qes: 1.16
Qms: 0.74

The voice coils of the woofer serving as P.R. are both open.

In response to Rodd Yamashita, response of the mike elements is specified as flat from 30 Hz to 2 kHz. The amplifiers are a configuraton of the NE5534 opamp. However unfortunately I don't have the equipment to really know the extent to which my measuring set-up is accurate.

Thanks to all for your feedback about this-

Pete

[roddyama]

Pete,

Since you're using a woofer (with VC) as a PR, connect your voltmeter to the PR's terminals and sweep the input frequency through the PR's range. The voltage output from the PR should at least give you an indication that the PR is moving and can show you the frequency where the PR's peak output is.

[MCPete]

Rodd,

Frequency corresponding to peak voltage taken across the input terminals of the driver serving as passive radiator is at least close to Fb, I assume. My semi-educated guess would be that how close the frequency of peak voltage is to Fb would be dependent on Qtc of the driver/ passive radiator.

However currently, to find Fb, I am using an oscilloscope functioning in X/Y mode where the "X" voltage is the output voltage of the sine wave source applied to a 680 Ohm resistor in series with the driver of the P.R. system and the "Y" voltage is the voltage drop across the driver. This set-up is also from the Loudspeaker Design Cookbook.

-Pete

[Ron E]

Here is a complete set of parameters (as connected) that would allow me to model.

Fs
Qts
Qes
Qms
Diameter
Re
Vas
Vb (per woofer)

If you want excursion modeling, Xmax and Rated power would need to be specified.

[MCPete]

Ron E,

As the driven DVC woofer in the system that I measured had the unusual configuration of one voice coil shorted, below are the parameters of the same woofer with the voice coils connected in parallel from the spec. sheet. This also results in Qts= 0.45 which is what the alignment that I tested required.

Fs: 45 HZ
Qts: 0.45
Qes: 0.50
Qms: 4.24
Diameter: Sd = 17 cm
Re: 6.0 Ohm
Vas: 17.8L
Vb (per woofer): 18.5L

Your "per woofer" qualification has me a little puzzled. The alignment calls for alpha= 0.96 which I take as meaning that internal volume should be equal to 1/0.96 times Vas. That is, one of the woofers driven and the other one passive means that the driven one "sees" the entire internal volume of air in the box as what it acts against.

Today I read an article by Small where he says that in testing vented systems, higher than predicted losses occurred even with systems that were well-built, the drivers had solid dust caps and driver-gaskets were air-tight.

In Weems' book Designing, Building & Testing Your Own Speaker System, in the chart for alpha corresponding to Qts for vented systems, alpha = 1.5 where Qts = 0.45. Weems says that this chart includes about 30% oversize to compensate for losses. So my conclusion is that I might fix my alignment by increasing Vb. When I get a chance I'm going to test that.

Thanks for your offer to computer simulate,
Pete

[Ron E]

In your first message you said 2 woofers. just making sure I understand you. One of the woofers serves as the PR, right?

Your simulated F3 is about 58Hz Doubling volume to 35liters would change your F3 to 56Hz. Basically, woofers do not make good PR's. For a PR you want a low resonant frequency, high Vap and High Qmp. If you used a port, you could get a F3 of ~43Hz in the 18L box.

Attached is a sim of your PR box, with a PDF of the plots.

Woofer parameters
Fs 45 Hz
Qts 0.45
Qes 1.16
Vas 17.8 Liters
Re 6 Ohms
Dia 17 cm
Xmax 5 mm
Pe_max 100 Watts
Le 0 Henries
P_input_rms 100 Watts@8ohms

Passive radiator free-air parameters
Fp 45 Hz
Vap 17.8 Liters
Dia 17 cm

Box parameters
Ql 15.0
Qb 20.0
Qp 2.9
Vb 18.5
Desired Fb 51.6

-------------------------frequency response----------------------
f dB_ref
10.0 -36.15
10.4 -35.58
10.7 -35.01
11.1 -34.44
11.5 -33.87
11.9 -33.31
12.3 -32.75
12.7 -32.20
13.2 -31.65
13.7 -31.11
14.1 -30.57
14.6 -30.03
15.2 -29.50
15.7 -28.98
16.2 -28.47
16.8 -27.96
17.4 -27.46
18.0 -26.97
18.7 -26.48
19.3 -26.01
20.0 -25.55
20.7 -25.11
21.4 -24.67
22.2 -24.25
23.0 -23.85
23.8 -23.46
24.6 -23.08
25.5 -22.73
26.4 -22.38
27.3 -22.05
28.3 -21.73
29.3 -21.41
30.3 -21.08
31.4 -20.72
32.5 -20.31
33.6 -19.81
34.8 -19.21
36.1 -18.45
37.3 -17.53
38.6 -16.46
40.0 -15.24
41.4 -13.92
42.9 -12.55
44.4 -11.17
45.9 -9.81
47.6 -8.51
49.2 -7.29
51.0 -6.19
52.8 -5.20
54.6 -4.34
56.6 -3.60
58.6 -2.98
60.6 -2.47
62.8 -2.05
65.0 -1.70
67.3 -1.43
69.6 -1.20
72.1 -1.01
74.6 -0.86
77.3 -0.73
80.0 -0.63
82.8 -0.54
85.7 -0.47
88.8 -0.40
91.9 -0.35
95.1 -0.31
98.5 -0.27
102.0 -0.23
105.6 -0.21
109.3 -0.18
113.1 -0.16
117.1 -0.14
121.3 -0.13
125.5 -0.11
130.0 -0.10
134.5 -0.09
139.3 -0.08
144.2 -0.07
149.3 -0.07
154.5 -0.06
160.0 -0.06
165.6 -0.05
171.5 -0.05
177.5 -0.05
183.8 -0.04
190.3 -0.04
197.0 -0.04
203.9 -0.04
211.1 -0.04
218.6 -0.03
226.3 -0.03
234.3 -0.03
242.5 -0.03
251.1 -0.03
259.9 -0.03
269.1 -0.03
278.6 -0.03
288.4 -0.03
298.6 -0.03
309.1 -0.03
320.0 -0.03
331.3 -0.03
343.0 -0.03
355.1 -0.03
367.6 -0.03
380.5 -0.03
394.0 -0.03
407.9 -0.03
422.2 -0.03
437.1 -0.03
452.5 -0.03
468.5 -0.03
485.0 -0.03
502.1 -0.03