Tech Design.....

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Dipoles and Open Baffle Design Considerations

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Dipoles and Open Baffle Design Considerations

This tutorial is directed at the discussion of dipole (DP) and open baffle (OB) speakers system employing flat

baffles, various design considerations and their differences and similarities. More specifically it is directed at

OB/DP midrange response and influencing factors. The discussion begins with point source drivers and moves

onwards to directional drivers with symmetric front and rear response. Consideration of drivers where the front

and rear responses are asymmetric, which may be likened to rear world drivers, is commented on briefly. Only

generalized results are presented yielding an indication of how various parameters influence the response.

Many of these aspects are discussed in other sections of this website, however here the attempt is to focus only

on DP and OB system. No consideration is given to room interaction in the discussion. The information will be

updated and expanded over time.

To begin, consider a two simple systems: a single point source (monopole) radiating into free space, and a

dipole composed ot two point sources separated by a distance, d, as shown in Figure 1. The monopole radiates

baffles, various design considerations and their differences and similarities. More specifically it is directed at

OB/DP midrange response and influencing factors. The discussion begins with point source drivers and moves

onwards to directional drivers with symmetric front and rear response. Consideration of drivers where the front

and rear responses are asymmetric, which may be likened to rear world drivers, is commented on briefly. Only

generalized results are presented yielding an indication of how various parameters influence the response.

Many of these aspects are discussed in other sections of this website, however here the attempt is to focus only

on DP and OB system. No consideration is given to room interaction in the discussion. The information will be

updated and expanded over time.

To begin, consider a two simple systems: a single point source (monopole) radiating into free space, and a

dipole composed ot two point sources separated by a distance, d, as shown in Figure 1. The monopole radiates

uniformly in all directions

at all frequencies. The

dipole has an on axis

response that appears as

shown below in Figure 2.

A dipole peak is present

at the frequency given by

**F**p = C/(2d)

The level of the dipole in

the 1/f region is equal to

that of monopole at a

frequency given by

**F**eq = C/(6d).

The peak frequency

occurs where the

at all frequencies. The

dipole has an on axis

response that appears as

shown below in Figure 2.

A dipole peak is present

at the frequency given by

The level of the dipole in

the 1/f region is equal to

that of monopole at a

frequency given by

The peak frequency

occurs where the

propagation delay is equal to 1/2 a period (the

separation is 1/2 a wave length) corresponding to a 180

degree phase delay.**F**eq occurs at the frequency

where the propagation delay is equal to 1/6 th of a

period, (60 degrees). Under such conditions the vector

sum of the front and rear radiation forms an equilateral

triangle with the resultant response vector. The polar

response of the dipole, far from the center of the dipole,

is as shown in Figure 3 as a function of the separation

divided by wave length, w. For long wavelengths,

separation is 1/2 a wave length) corresponding to a 180

degree phase delay.

where the propagation delay is equal to 1/6 th of a

period, (60 degrees). Under such conditions the vector

sum of the front and rear radiation forms an equilateral

triangle with the resultant response vector. The polar

response of the dipole, far from the center of the dipole,

is as shown in Figure 3 as a function of the separation

divided by wave length, w. For long wavelengths,

(low frequency) d/W is

small and the radiation

pattern is the classical

dipole figure 8. This

pattern remains fairly

constant up to about

d/w = 0.25, or an octave

below the dipole peak.

Above d/w = 0.25 the

radiation pattern initially

broadens up to about d/w

= 0.66 with an off axis

bulge before degenerating

into a multi-lobed

response. The number of

lobes above d/w = 1.0 will

increase as the value of

d/w increases. Figure 3

shows the result for d/w =

1. which corresponds the

frequency of the first null

above the dipole peaks in

Figure 2.

One of the common

misconceptions about

dipoles is that they have

constant directivity thus

can be equalized to yield

small and the radiation

pattern is the classical

dipole figure 8. This

pattern remains fairly

constant up to about

d/w = 0.25, or an octave

below the dipole peak.

Above d/w = 0.25 the

radiation pattern initially

broadens up to about d/w

= 0.66 with an off axis

bulge before degenerating

into a multi-lobed

response. The number of

lobes above d/w = 1.0 will

increase as the value of

d/w increases. Figure 3

shows the result for d/w =

1. which corresponds the

frequency of the first null

above the dipole peaks in

Figure 2.

One of the common

misconceptions about

dipoles is that they have

constant directivity thus

can be equalized to yield

constant power. As shown in Figure 3,

this is strictly true only for frequencies

for which d/w is less than 0.25 and even

then there is some minor variation with

frequency. However, we can take the

power as constant below this point and

equal to 4.8 dB less than an omni

directional source with the same on axis

response. At the dipole peak an

unequalized dipole has an on axis

response of +6 dB. At the same

frequency the radiated power is 3 dB

greater than an omni directional source.

When equalized to have the same level

as the omni source at this frequency

the dipole radiates only 3dB less power.

This is 1.8 dB greater than the radiated

power below d/w = 0.25.

Obviously, we can not equalize the

response flat above the dipole peak

due to the nulls and peaks and the

multi-lobed radiation pattern. However,

Figure 4 shows that for the unequalized

dipole the power response degenerates

to that ot two uncorrelated, omni

this is strictly true only for frequencies

for which d/w is less than 0.25 and even

then there is some minor variation with

frequency. However, we can take the

power as constant below this point and

equal to 4.8 dB less than an omni

directional source with the same on axis

response. At the dipole peak an

unequalized dipole has an on axis

response of +6 dB. At the same

frequency the radiated power is 3 dB

greater than an omni directional source.

When equalized to have the same level

as the omni source at this frequency

the dipole radiates only 3dB less power.

This is 1.8 dB greater than the radiated

power below d/w = 0.25.

Obviously, we can not equalize the

response flat above the dipole peak

due to the nulls and peaks and the

multi-lobed radiation pattern. However,

Figure 4 shows that for the unequalized

dipole the power response degenerates

to that ot two uncorrelated, omni

directional sources at a level 3dB greater than a single source. The power is independent of the format, dipole or

otherwise, in the uncorrelated region. Thus, even before we consider the roll of a baffle in creating a dipole with

a conventional driver it must be recognized that if constant radiated power is an objective there is a need to

proceed with caution. This is of particular concern if it is desired to use the response above the dipole peak.

**Circular Baffle Dipoles with Omni Sources.**

The first step is to understand the roll of a circular baffle in the formation of a "dipole like" response. Rather than

separating two omni sources by a distance, d, to form a dipole a circular baffle of radius d can be substituted.**On **

axis the propagation of the wave from the rear source to the baffle edge results in a delay equal to that which

would occur if the sources were separated. Thus the on axis response will appear identical to that shown in

otherwise, in the uncorrelated region. Thus, even before we consider the roll of a baffle in creating a dipole with

a conventional driver it must be recognized that if constant radiated power is an objective there is a need to

proceed with caution. This is of particular concern if it is desired to use the response above the dipole peak.

separating two omni sources by a distance, d, to form a dipole a circular baffle of radius d can be substituted.

axis

would occur if the sources were separated. Thus the on axis response will appear identical to that shown in

Figure 2. However, off axis there will

be significant differences. For the

true dipole, as we move off axis the

effective separation between the

sources varies as d' = d cos(theta)

where theta is the off axis angle.

Thus, when theta = 90 degrees the

effective separation goes to zero and

the sources, being of inverted

polarity, will cancel exactly yielding

the 90 degree null. At 45 degrees off

axis the effective separation is

reduced to 0.707d and the result is a

shifting to the dipole peak 1/2 octave

higher, at 60 degrees off axis the

effective separation is reduced to

0.5d moving the dipole peak a full

octave higher. Figure 6 shows the

ramification of this behavior.

be significant differences. For the

true dipole, as we move off axis the

effective separation between the

sources varies as d' = d cos(theta)

where theta is the off axis angle.

Thus, when theta = 90 degrees the

effective separation goes to zero and

the sources, being of inverted

polarity, will cancel exactly yielding

the 90 degree null. At 45 degrees off

axis the effective separation is

reduced to 0.707d and the result is a

shifting to the dipole peak 1/2 octave

higher, at 60 degrees off axis the

effective separation is reduced to

0.5d moving the dipole peak a full

octave higher. Figure 6 shows the

ramification of this behavior.

The lowering of the response level in the 1/f region is apparent, but as we move off axis and the dipole peak

moves to a higher frequency the effect is obvious. Conversely, as shown in Figure 7, moving off axis for the

circular baffle dipole has the same effect at low frequency while resulting in smoother response at higher

frequency. This is a consequence of the fact that the circular baffle dipole operates very much like a point source

surrounded by a ring radiator where the integrated strength of the ring radiator around the baffle edge is equal

to that of the point source in the center, but of opposite polarity. This analogy is reasonable on axis and for

moderate off axis angles but will ultimately fail as the off axis angle approaches 90 degrees. The reason for the

observed behavior should be obvious: the path length form all points on the ring radiator to any point**on the **

dipole axis is the same. However, when we move off axis the path length from different positions on ring radiator

to the observation point will vary. Since the on axis case is the worst case, resulting in 6dB peaks and nulls above

the dipole peak, moving off axis can only improve the situation, with a reduction in the peaks and a filling of the

nulls. If we change our thinking to the time domain, then the impulse response of the unequalized, circular baffle

dipole looks like the blue trace in Figure 8 on axis. At 45 degrees off axis it appears as shown by the red trace

where the inverted impulse form the ring radiator is scattered or smeared over time. While on the subject

moves to a higher frequency the effect is obvious. Conversely, as shown in Figure 7, moving off axis for the

circular baffle dipole has the same effect at low frequency while resulting in smoother response at higher

frequency. This is a consequence of the fact that the circular baffle dipole operates very much like a point source

surrounded by a ring radiator where the integrated strength of the ring radiator around the baffle edge is equal

to that of the point source in the center, but of opposite polarity. This analogy is reasonable on axis and for

moderate off axis angles but will ultimately fail as the off axis angle approaches 90 degrees. The reason for the

observed behavior should be obvious: the path length form all points on the ring radiator to any point

dipole axis

to the observation point will vary. Since the on axis case is the worst case, resulting in 6dB peaks and nulls above

the dipole peak, moving off axis can only improve the situation, with a reduction in the peaks and a filling of the

nulls. If we change our thinking to the time domain, then the impulse response of the unequalized, circular baffle

dipole looks like the blue trace in Figure 8 on axis. At 45 degrees off axis it appears as shown by the red trace

where the inverted impulse form the ring radiator is scattered or smeared over time. While on the subject

of the impulse response we should also look briefly at the impulse

response of the dipole on axis, with and w/o equalization for flat

response, as shown in Figure 9. Equalization of the dipole for flat

response in the 1/f region results in turning the double impulse of

the unequalized dipole (blue) into a finite width pulse with the pulse

width equal to the delay between sources. Thus the equalized

dipole time smears the impulse response. This is a characteristic

of the equalized dipole and is not related to room effects. Figures 8

response of the dipole on axis, with and w/o equalization for flat

response, as shown in Figure 9. Equalization of the dipole for flat

response in the 1/f region results in turning the double impulse of

the unequalized dipole (blue) into a finite width pulse with the pulse

width equal to the delay between sources. Thus the equalized

dipole time smears the impulse response. This is a characteristic

of the equalized dipole and is not related to room effects. Figures 8

and 9 represent what would be measured on and off axis for unequalized and equalized circular baffle dipoles

using omni sources. Obviously equalization above the 1/f region is not possible due to the nature of the

response.

**Non Circular Baffles with Omni Sources:**

The behavior of the circular baffle response off axis suggests that the on axis response of a dipole composed of

omni sources could be smoothed somewhat if the rear wave could be scattered relative to the on axis position.

The use of an irregularly shaped baffle can accomplish this task since relative to a position on axis the delay will

vary around the baffle circumference. Additionally, as discussed elsewhere on this web site, below the dipole

peak it can be shown that irregularly shaped baffles are equivalent to circular baffles at low frequency with

respect to frequency response and level. Thus, an irregularly shaped baffle can help smooth the on axis

response above the dipole peak without loss of low frequency sensitivity, compared to the equivalent circular

baffle. We need not go to extremes here. A rectangular baffle can provide a significant improvement, and

positioning the driver so that it is centered horizontally will assure left-right symmetry in the response. Figure 10

shows such a case for omni front and rear sources. The sources are centered on a rectangular baffle with

dimensions chosen such that at low frequency the equivalent diameter is that of the circular baffle considered

above while the height and width were selected to yield a smoother response between 500 and 2 K Hz, both on

axis (blue), and out to 25 degrees off axis (green). The red line is the circular baffle result. In this example the

baffle was 20 cm wide and 52 cm high. The plot represents the result far from the baffle.* (The lack of the deep *

nulls in the circular baffle result of this figure is due to the frequency resolution of the simulation.)

using omni sources. Obviously equalization above the 1/f region is not possible due to the nature of the

response.

omni sources could be smoothed somewhat if the rear wave could be scattered relative to the on axis position.

The use of an irregularly shaped baffle can accomplish this task since relative to a position on axis the delay will

vary around the baffle circumference. Additionally, as discussed elsewhere on this web site, below the dipole

peak it can be shown that irregularly shaped baffles are equivalent to circular baffles at low frequency with

respect to frequency response and level. Thus, an irregularly shaped baffle can help smooth the on axis

response above the dipole peak without loss of low frequency sensitivity, compared to the equivalent circular

baffle. We need not go to extremes here. A rectangular baffle can provide a significant improvement, and

positioning the driver so that it is centered horizontally will assure left-right symmetry in the response. Figure 10

shows such a case for omni front and rear sources. The sources are centered on a rectangular baffle with

dimensions chosen such that at low frequency the equivalent diameter is that of the circular baffle considered

above while the height and width were selected to yield a smoother response between 500 and 2 K Hz, both on

axis (blue), and out to 25 degrees off axis (green). The red line is the circular baffle result. In this example the

baffle was 20 cm wide and 52 cm high. The plot represents the result far from the baffle.

nulls in the circular baffle result of this figure is due to the frequency resolution of the simulation.)

baffles. We have seen that using an irregularly shaped baffle can yield smoother response above the dipole

peak, both on and off axis, compared to an circular baffle with the same equivalent radius. The reason for this

is straight forward, as discussed, and is due to the varying delays from the different positions around the baffle

edge. However, there is another factor which must be considered when using real drivers on an opened baffle;

driver directionality. As the radiated frequency increases a driver becomes directional. As a result, since the

radiation from the rear of the baffle is dependent on the 90 degree off axis response of the driver, the

response of the "ring radiator" will generally weaken as the frequency rises. Figure 11 shown the theoretical 90

degree off axis response for a 6" flat piston in blue and a crude approximation to the response in red. The on

axis response of a dipole using such a driver on a

30 cm circular baffle is shown in Figure 12. As can

be observed, the response is much smoother above

the dipole peak than the omni directional driver

shown in red in Figure 10 and is even smoother

than the omni directional driver mounted on a

rectangular baffle as shown in blue in Figure 10.

This is because the rear response reaching the on

axis position is effectively low pass filtered and there

is a loss of the dipole response above the on axis

peak for this driver/baffle size combination.

The impulse response for this system is shown in

Figure 13. At the left of Figure 13 the impulse for the

unequalized response is presented. The negative

pulse from the rear reflects the low pass filtering

effect. This should be compared with the blue trace

in Figure 9. The impulse when the response of

Figure 12 is equalized flat is presented at the right

of Figure 13. This should be compared to the red

trace of Figure 9. This is clearly an

30 cm circular baffle is shown in Figure 12. As can

be observed, the response is much smoother above

the dipole peak than the omni directional driver

shown in red in Figure 10 and is even smoother

than the omni directional driver mounted on a

rectangular baffle as shown in blue in Figure 10.

This is because the rear response reaching the on

axis position is effectively low pass filtered and there

is a loss of the dipole response above the on axis

peak for this driver/baffle size combination.

The impulse response for this system is shown in

Figure 13. At the left of Figure 13 the impulse for the

unequalized response is presented. The negative

pulse from the rear reflects the low pass filtering

effect. This should be compared with the blue trace

in Figure 9. The impulse when the response of

Figure 12 is equalized flat is presented at the right

of Figure 13. This should be compared to the red

trace of Figure 9. This is clearly an

improvement over the characteristic of an omni source. The

reason is that the response ceases to be of a dipole nature

above the frequency where the driver becomes directional

*provided* that the baffle is sized such that the dipole peak is at a

frequency where directionality is becoming significant.

As a further example, consider the same driver model on a 60

cm diameter circular baffle. This places the dipole peak one

octave lower with an on axis frequency response that appears

as shown in red in Figure 14. While we observe an improvement

reason is that the response ceases to be of a dipole nature

above the frequency where the driver becomes directional

frequency where directionality is becoming significant.

As a further example, consider the same driver model on a 60

cm diameter circular baffle. This places the dipole peak one

octave lower with an on axis frequency response that appears

as shown in red in Figure 14. While we observe an improvement

than the corresponding dip (at 2k Hz) for the 30 cm baffle. This is because the driver is closer to an omni

directional source at 1k Hz, as is apparent from Figure 11.The impulse response for the unequalized 60 cm

baffle is shown in Figure 15. It is identical to that at the left of Figure 13 except the rear pulse is delayed twice

as long. The greater irregularity in the response would likely prevent use of this baffle /driver configuration

even if suitable equalization to flatten the response were applied. It just isn't a good starting point. However

several important observations can be made. First, the directional characteristics of the driver determine the

frequency limit above which true dipole operation can be obtained from a specific driver. Above that

frequency the characteristics of the front and rear radiation are dominated by the directional characteristics

of the driver and diffraction from the baffle edge is much more like that for a conventional speaker. Second,

with a circular baffle, the baffle diameter will set the frequency of the dipole peak, and more importantly, the

frequency of that peak in relation to the frequency above which the driver becomes directional will determine

the characteristic of the response at higher frequency. Third, while a larger baffle will increase the low

frequency sensitivity the greater delay will translate a smearing of the impulse response over a longer period

of time.

Since a larger circular baffle results in lowering the dipole peak to a frequency where the response just

above the peak behaves more like that for an omni source the same approach to smoothing the response is

appropriate; smear the rear response over time by using a rectangular baffle. Figure 16 shows the response

of the 60 cm circular baffle in blue and that for a rectangular baffle of the same equivalent radius in red. The

driver was centered on the rectangular baffle which was 40 cm wide and 76 cm high. As can be seen,

directional source at 1k Hz, as is apparent from Figure 11.The impulse response for the unequalized 60 cm

baffle is shown in Figure 15. It is identical to that at the left of Figure 13 except the rear pulse is delayed twice

as long. The greater irregularity in the response would likely prevent use of this baffle /driver configuration

even if suitable equalization to flatten the response were applied. It just isn't a good starting point. However

several important observations can be made. First, the directional characteristics of the driver determine the

frequency limit above which true dipole operation can be obtained from a specific driver. Above that

frequency the characteristics of the front and rear radiation are dominated by the directional characteristics

of the driver and diffraction from the baffle edge is much more like that for a conventional speaker. Second,

with a circular baffle, the baffle diameter will set the frequency of the dipole peak, and more importantly, the

frequency of that peak in relation to the frequency above which the driver becomes directional will determine

the characteristic of the response at higher frequency. Third, while a larger baffle will increase the low

frequency sensitivity the greater delay will translate a smearing of the impulse response over a longer period

of time.

Since a larger circular baffle results in lowering the dipole peak to a frequency where the response just

above the peak behaves more like that for an omni source the same approach to smoothing the response is

appropriate; smear the rear response over time by using a rectangular baffle. Figure 16 shows the response

of the 60 cm circular baffle in blue and that for a rectangular baffle of the same equivalent radius in red. The

driver was centered on the rectangular baffle which was 40 cm wide and 76 cm high. As can be seen,

in the low

frequency

sensitivity, which

is the main reason

for selecting a

larger baffle, we

also note that the

dip in the

response at 1k Hz

is much deeper

frequency

sensitivity, which

is the main reason

for selecting a

larger baffle, we

also note that the

dip in the

response at 1k Hz

is much deeper

the rectangular baffle has the same low frequency

characteristic but results in a relatively smooth

response above the dipole peak, thus requiring

minimal equalization consisting of 6dB/octave boost

below the peak and a Q bump filter to flatten the peak.

The impulse response for this baffle/driver combination

for the unequalized (red)and equalized to flat (blue)

cases is shown in Figure 17. The unequalized

characteristic but results in a relatively smooth

response above the dipole peak, thus requiring

minimal equalization consisting of 6dB/octave boost

below the peak and a Q bump filter to flatten the peak.

The impulse response for this baffle/driver combination

for the unequalized (red)and equalized to flat (blue)

cases is shown in Figure 17. The unequalized

impulse (red) has a characteristic similar to that of the circular baffle shown

in Figure 15 however the negative pulse is lower in amplitude and extends

over a longer time period because of the variable delay around the

perimeter of the baffle. Considering the 6dB increase in low frequency

sensitivity compared to the 30 cm circular baffle of Figure 15 which also had

acceptably smooth response above the dipole peak, it might be expected

that such a configuration would be superior. However, there is another

factor to consider; power response.

in Figure 15 however the negative pulse is lower in amplitude and extends

over a longer time period because of the variable delay around the

perimeter of the baffle. Considering the 6dB increase in low frequency

sensitivity compared to the 30 cm circular baffle of Figure 15 which also had

acceptably smooth response above the dipole peak, it might be expected

that such a configuration would be superior. However, there is another

factor to consider; power response.

consider one dipole and the other simply an open baffle design. The desire to go to an open baffle is usually

motivated by a desire to eliminate box colorations. However, when power response is considered it is possible

to differentiate further by considering the variation of radiated power with frequency. As discussed at the

beginning of this tutorial the widely accepted view is that a dipole radiates 4.8dB less acoustic power than an

omni directional source with the same on axis response. However, this only applies from approximately one

octave below the dipole peak and lower, providing the driver is effectively omni directional over that frequency

range. As the frequency goes higher the power response may begin to rise.

Consider the power radiated by the configuration of Figure 12, a directional driver on a 30 cm circular baffle,

and that of Figure 16, the same driver on a rectangular baffle with 60 cm equivalent radius. If constant power

vs frequency is desired which configuration is superior? The answer is obviously dependent on the crossover

frequency and driver directional characteristics, but the baffle configuration must also be considered. The

radiated power for the larger rectangular baffle would appear something like that shown in

The power is constant at

low frequency but then

rises to a peak at about

1k Hz before falling off

due to the driver's

directional characteristics.

The power response for

the smaller circular baffle

is shown in red. It shows a

relatively constant power

level until beginning to fall

off at higher frequency.

The corresponding

horizontal polar

responses at 1k Hz are

shown at the right. Not

only is the polar response

broadening for the larger

baffle, the off axis

response is actually at a

greater level than the on

axis response. All of this

results because with the

larger baffle the

frequency of the dipole

peak is pushed down to a

frequency where the

driver is still radiating in

low frequency but then

rises to a peak at about

1k Hz before falling off

due to the driver's

directional characteristics.

The power response for

the smaller circular baffle

is shown in red. It shows a

relatively constant power

level until beginning to fall

off at higher frequency.

The corresponding

horizontal polar

responses at 1k Hz are

shown at the right. Not

only is the polar response

broadening for the larger

baffle, the off axis

response is actually at a

greater level than the on

axis response. All of this

results because with the

larger baffle the

frequency of the dipole

peak is pushed down to a

frequency where the

driver is still radiating in

an omni directional manner and the radiation pattern balloons as it would for a true dipole (see Figures 2 and

3 above) before driver directionality counters this effect. This may result in an over aggressive sounding

upper midrange when large baffles are implemented to improve low frequency sensitivity and at the same time

taking the observed smoothness of the on axis response as an indication that the crossover can be pushed to

a higher frequency. With the smaller baffle the tendency for the polar response to balloon at, and initially

above the dipole peak, is countered by the directional characteristics of the driver resulting in a more uniform

power response. Thus, while the larger baffle results in a 6dB increase in low frequency sensitivity, extending

the useful low frequency limit for a given maximum SPL by an octave, this is offset by the requirement that the

useful high frequency limit is reduced by an octave**or more** if constant radiated power is desired. If we take

the power response plots above as reasonable, then for the two baffles considered the high frequency

limitation would be of the order of 1.5K Hz for the smaller baffle and around 400 Hz for the larger baffle. Over

all this would mean that form the power response point of view the same driver mounted on a the smaller

baffle would have useful bandwidth about one octave wider than when mounted on the larger baffle in spite of

the apparent smoothness of the on axis response.

**Closing Comments:**

The discussion presented above is based on theoretical considerations only. As such it provides insight into

the behavior of open baffle and dipole speaker designs based on conventional drivers which should be taken

into consideration for any such design. Other factors also enter the picture which have not been discussed.

hopefully these will be expanded upon in the future. For example, all the cases above assume that the

radiation from the front and rear of the driver is identical in amplitude and inverted in phase. When real drivers

are considered any asymmetry between the front and rear response must be considered as well. Since such

effect are largely dependent on the specific driver and are generally unpredictable, there can be no substitute

for testing and measurement of any given design both on and off axis.

3 above) before driver directionality counters this effect. This may result in an over aggressive sounding

upper midrange when large baffles are implemented to improve low frequency sensitivity and at the same time

taking the observed smoothness of the on axis response as an indication that the crossover can be pushed to

a higher frequency. With the smaller baffle the tendency for the polar response to balloon at, and initially

above the dipole peak, is countered by the directional characteristics of the driver resulting in a more uniform

power response. Thus, while the larger baffle results in a 6dB increase in low frequency sensitivity, extending

the useful low frequency limit for a given maximum SPL by an octave, this is offset by the requirement that the

useful high frequency limit is reduced by an octave

the power response plots above as reasonable, then for the two baffles considered the high frequency

limitation would be of the order of 1.5K Hz for the smaller baffle and around 400 Hz for the larger baffle. Over

all this would mean that form the power response point of view the same driver mounted on a the smaller

baffle would have useful bandwidth about one octave wider than when mounted on the larger baffle in spite of

the apparent smoothness of the on axis response.

the behavior of open baffle and dipole speaker designs based on conventional drivers which should be taken

into consideration for any such design. Other factors also enter the picture which have not been discussed.

hopefully these will be expanded upon in the future. For example, all the cases above assume that the

radiation from the front and rear of the driver is identical in amplitude and inverted in phase. When real drivers

are considered any asymmetry between the front and rear response must be considered as well. Since such

effect are largely dependent on the specific driver and are generally unpredictable, there can be no substitute

for testing and measurement of any given design both on and off axis.