Eldartford,
My apologies again for yesterday's outbreaks, it was a pretty rough day and I'm not the best at being calm anyway. A good night's rest helps a lot.
To try to explain what I was after:
In the parallel case, you have two separate filters, LR and CR, which both have Butterworth responses by default (maximally flat, Q=0.7). You can change L or C, and it will change the corner frequency but not the Q of the filter, and it does not affect the other filter at all. On the other hand, it does affect the voltage sum of the two drivers, which affects the summed frequency response.
In the series case, you have the equivalent of an LCR loop, which is a resonant circuit. (It's not the simplest form of LCR, but it's a loop nonetheless.) Now if you stick to Butterworth values for L and C, you have an equivalence to the parallel case, and everything works the same. However, in an LCR loop, the resonant frequency is singular and is determined by the product of L and C. In addition, the loop has a resonant Q which is determined by the ratio between L and C. What this means is that you can double one, and halve the other, and end up with the same resonant frequency but a different Q. So it doesn't behave the same as a parallel except in the case where you use standard Butterworth values. Also in contrast to the parallel network, the series network by its very nature maintains a constant voltage sum across the drivers, which maintains flat frequency response despite the variations in the components.
Of course, there are a lot of assumptions built into all of this, such as equal resistive drivers, equal amplitude and phase response, constant voltage source, etc., none of which are really achieved in the real world. That is why I view the series as being superior to the parallel, because it automatically minimizes the effects of at least some of these "non-perfect" conditions.
Best Regards,
Karl
My apologies again for yesterday's outbreaks, it was a pretty rough day and I'm not the best at being calm anyway. A good night's rest helps a lot.
To try to explain what I was after:
In the parallel case, you have two separate filters, LR and CR, which both have Butterworth responses by default (maximally flat, Q=0.7). You can change L or C, and it will change the corner frequency but not the Q of the filter, and it does not affect the other filter at all. On the other hand, it does affect the voltage sum of the two drivers, which affects the summed frequency response.
In the series case, you have the equivalent of an LCR loop, which is a resonant circuit. (It's not the simplest form of LCR, but it's a loop nonetheless.) Now if you stick to Butterworth values for L and C, you have an equivalence to the parallel case, and everything works the same. However, in an LCR loop, the resonant frequency is singular and is determined by the product of L and C. In addition, the loop has a resonant Q which is determined by the ratio between L and C. What this means is that you can double one, and halve the other, and end up with the same resonant frequency but a different Q. So it doesn't behave the same as a parallel except in the case where you use standard Butterworth values. Also in contrast to the parallel network, the series network by its very nature maintains a constant voltage sum across the drivers, which maintains flat frequency response despite the variations in the components.
Of course, there are a lot of assumptions built into all of this, such as equal resistive drivers, equal amplitude and phase response, constant voltage source, etc., none of which are really achieved in the real world. That is why I view the series as being superior to the parallel, because it automatically minimizes the effects of at least some of these "non-perfect" conditions.
Best Regards,
Karl