High Performances Crossovers for Professional Loudspeaker Systems and their Real World applications By Mario Di Cola, Audio Labs Systems, Milano, Italia Senior Loudspeaker System Engineer mdicola@lisasystem.com ALMA European Symposium, Frankfurt, April 2009 Derived by the AES Paper Presented by M. Di Cola, M. Hadelich, D. Ponteggia and D. Saronni at 121st AES Convention, October 2006, San Francisco, USA
Multi way systems Almost the totality of Sound Reinforcement Loudspeaker Systems are multi way systems For several reasons one single transducer cannot reproduce the entire Audio Bandwidth The way the crossover is made is deeply influencing the final performances of the Loudspeaker System
Why a system need to be multi-way? How the cross-over should be designed?
Why a system need to be multi-way? How the cross-over should be designed? Subwoofer Low-Mid Cone High Frequency Driver High Frequency Driver Subwoofer Low-Mid Cone
One simple question: What happens to the signal passing through a Crossover Filter?
Sine wave through a Linear System Transfer Function Input Output Linear System time
Sine wave through a Linear System Transfer Function Input Output Linear System
Sine wave through a Linear System: effect of Phase Shift in Filters Input Output Linear System Example 1: Frequency inside the Pass-Band
Sine wave through a Linear System: effect of Phase Shift in Filters Input Output Linear System Example 2: Frequency close to the cut frequency
Sine wave through a Linear System: effect of Phase Shift in Filters Input Output Linear System Example 2: Frequency outside the Pass-Band
Sine wave through a Linear System: effect of Phase Shift in Filters
Desired Target Response at any crossover point: a simple example of a optimal summation between 2 perfectly symmetrical responses of 4th Order (24dB/Oct), Linkwitz-Riley
How the Crossover Approach can affect the Loudspeaker Time Alignment? HF Arrival Wavelet Analysis Diagram Crossover Point Frequency LF Energy Arrival Time
A simple symmetric Crossover: 2nd Order, L-R Type Low Pass Filter
A simple symmetric Crossover: 2nd Order, L-R Type High Pass Filter
4th Order L-R Symmetric Crossover 2nd Order 2nd Order 2nd Order 2nd Order
4th Order L-R Symmetric Crossover High Pass Filter + 180 deg Low Pass Filter - 180 deg
4th Order L-R Symmetric Crossover Overall Phase Relationship between the two outputs could be more clear using a +360-360 phase diagram + 360 deg High Pass Filter Low Pass Filter - 360 deg
Drivers Time alignment in different Crossover Design strategies applied to a sample 2 way system All-Pass Network Crossover (Only geometric Issues are taken in count while Time Aligning the drivers and then Phase Alignment is usually obtained delaying the woofer ) Actual Position: effect of Low Pass Group Delay Added to the driver delay Delaying the Closer Speaker Desired Time Origin
Drivers Time alignment in different Crossover Design strategies applied to a sample 2 way system Delay Compensated Crossover: (LP Filter Group Delay is taken in count in Drivers Time Alignment) Type 1 Typically smaller delay, but HF Polarity reversed Desired Time Origin Effect of Filter Group Delay
Drivers Time alignment in different Crossover Design strategies applied to a sample 2 way system Delay Compensated Crossover: (LP Filter Group Delay is taken in count in Drivers Time Alignment) Type 2 Typically larger delay, with HF in straight Polarity Desired Time Origin Effect of Filter Group Delay
Drivers Time alignment in different Crossover Design strategies applied to a sample 2 way system Linear Phase Filters Crossover (Only geometric Issues need to be taken in count while Time Aligning the drivers since Group Delay remains constant at any frequency) Delaying the Closer Speaker Desired Time Origin
Crossover Techniques comparison A quick review on relationship between Time Response and Transfer Function Analysis of practical application of different crossover strategies to the sample 2-way loudspeaker system
Ideal System Step Response and Relative Transfer Function: A Minimum Phase System
4th Order Butterworth High Pass (24dB/Oct) Response. Step Response and Relative Transfer Function: Still a Minimum Phase System Typical Response for a Bass Reflex aligned loudspeaker
6th Order Butterworth High Pass (36dB/Oct) Response. Step Response and Relative Transfer Function: Still a Minimum Phase System Typical Response for a High Pass Filtered Bass Reflex loudspeaker
Loudspeaker System Used for the Setup A simple 2-way Professional Loudspeaker System
Example 1: All-Pass Network Crossover Step Response Square Wave Response
Example 1: All-Pass Network Crossover Step Response Wavelet Analysis
Example 1: All Pass Network Crossover Vertical Polar Directivity Map [deg] Angle [db] Level 90 0 75 60-5 45 30 15-10 0-15 -15-30 -45-20 -60-75 -25-90 500 1k 2k 5k 10k Level Marker: z= -6 db Frequency [Hz]
6th Order Butterworth High Pass (36dB/Oct) Response. Step Response and Relative Transfer Function: NOT a Minimum Phase System
Step Response of different order Comparison Ideal System Step Response 4th Order HP Minimum Phase System 6th Order HP Minimum Phase System 6th Order HP All Pass Network System: Non Minimum Phase
Example 2: Delay Compensated Type 1 Step Response Square Wave Response
Example 2: Delay Compensated Type 1 Step Response Wavelet Analysis
Example 2: Delay Compensated Type 1 Vertical Polar Directivity Map [deg] Angle [db] Level 90 0 75 60-5 45 30 15-10 0-15 -15-30 -45-20 -60-75 -25-90 500 1k 2k 5k 10k Level Marker: z= -6 db Frequency [Hz]
Example 3: Delay Compensated Type 2 Step Response Square Wave Response
Example 3: Delay Compensated Type 2 Step Response Wavelet Analysis
Example 3: Delay Compensated Type 2 Vertical Polar Directivity Map [deg] Angle [db] Level 90 0 75 60-5 45 30 15-10 0-15 -15-30 -45-20 -60-75 -25-90 500 1k 2k 5k 10k Level Marker: z= -6 db Frequency [Hz]
Example 4: Linear Phase Filters Step Response Square Wave Response
Example 4: Linear Phase Filters Step Response Wavelet Analysis
Example 4: Linear Phase Filters Vertical Polar Directivity Map [deg] Angle [db] Level 90 0 75 60-5 45 30 15-10 0-15 -15-30 -45-20 -60-75 -25-90 500 1k 2k 5k 10k Level Marker: z= -6 db Frequency [Hz]
Transfer Functions Comparison All Pass Network Delay Compensated Type 2 Delay Compensated Type 1 Linear Phase Filters 24dB/Oct approx.
500 1k 1k 1k 1k 2k 2k 2k 2k 5k 5k 5k 5k Level Marker: z= -6 db Level Marker: z= -6 db Level Marker: z= -6 db Level Marker: z= -6 db 10k Frequency [Hz] [db] Level 10k Frequency [Hz] [db] Level 10k Frequency [Hz] [db] Level 10k Frequency [Hz] [db] Level -25-20 -15-10 -5 0-25 -20-15 -10-5 0-25 -20-15 -10-5 0-25 -20-15 -10-5 0 LIN PHASE DLY Type2 DLY Type1 ALL PASS -90-75 -60-45 -30-15 0 15 30 45 60 75 [deg] Angle 500 [deg] Angle 500 [deg] Angle 500 [deg] Angle 90-90 -75-60 -45-30 -15 0 15 30 45 60 75 90-90 -75-60 -45-30 -15 0 15 30 45 60 75 90-90 -75-60 -45-30 -15 0 15 30 45 60 75 90 Crossover Comparison
Further Improvements Performaces of the Linear Phase Filter processed version can be further improved in terms of vertical directivity control Steeper filter functions, in fact, can be introduced without additional phase distortion Additional advantages in terms of Power handling and reduced Distortion can be introduced by steeper crossover filters
Linear Phase Filters 24dB/Oct Square Wave Response Vertical Polar Direcivity Map [deg] Angle [db] Level 90 0 Wavelet Analysis 75 60-5 45 30 15-10 0-15 -15-30 -45-20 -60-75 -25-90 500 1k 2k 5k 10k Level Marker: z= -6 db Frequency [Hz]
Linear Phase Filters 74dB/Oct Square Wave Response Vertical Polar Direcivity Map [deg] Angle [db] Level 90 0 Wavelet Analysis 75 60-5 45 30 15-10 0-15 -15-30 -45-20 -60-75 -25-90 500 1k 2k 5k 10k Level Marker: z= -6 db Frequency [Hz]
Example of practical measurements Practical, real world transfer function measurements using a dedicated Dual Channel, FFT Analyzer
Comparison between All-Pass Network and Linear Phase Filters settings: Magnitude and Phase Response All-Pass Network Linear Phase Network
All-Pass Network Crossover settings: Magnitude and Phase Response showing each individual speaker contribution High Freq. Contribution Low Freq. Contribution
Linear Phase Filters Crossover settings: Magnitude and Phase Response showing each individual speaker contribution High Freq. Contribution Low Freq. Contribution
Magnitude and Phase response comparison Between: Delay Compensated Type 1, Type 2 and Linear Phase Filters Linear Phase Filters Delay Compensated Type 1 Delay Compensated Type 2
An example of how Delay Compensated Techniques can be adopted in order to match a Low Frequency extending unit to a Linear Phase Filters processed system Upper Band Response Subwoofer Response
An example of how Delay Compensated Techniques can be adopted in order to match a Low Frequency extending unit to a Linear Phase Filters processed system Reduced Phase Shift Subwoofer Plus upper system Crossover point
A simple direct advantage of minimizing overall phase shift
An All-Pass Crossover 2 way speaker Images taken from the AES Paper Written by Justin Baird and David McGrath about Linear Phase Filters advantages
An All-Pass Crossover 3 way speaker Images taken from the AES Paper Written by Justin Baird and David McGrath about Linear Phase Filters advantages
Effect of summation of the two speaker in the overlapping area Images taken from the AES Paper Written by Justin Baird and David McGrath about Linear Phase Filters advantages
Example of application of Linear Phase filters to an existing system.
Example of application of Linear Phase filters to an existing system LF MF MF LF HF Schematic view of the existing 3 way system used for the practical application
3 Way System Processing Comparison Original Preset Processing Linear Phase Filters Processing
3 Way System Processing Comparison Original Preset Processing Linear Phase Filters Processing
Additional Test Results Step Response Step Response Original Preset Processing Linear Phase Filters Processing Horizontal Polar Direcivity Map Horizontal Polar Direcivity Map
Results Some advantages can be achieved while processing loudspeaker systems with Linear Phase Filters Reducing the overall phase shift of a loudspeaker system response can result in better sound quality due to improved time coherence It was found that good and encouraging results can be obtained applying this technique to Concert Sound Reinforcement Systems: better array-ability properties and directivity control can be achieved beside improved sound quality Linear Phase Crossover is presently something readily available for anybody. By the way transforming Classic Filters based Crossover into a Linear Phase Crossover requires some accurate measurement and some careful attention, in order to be properly done
An Example on Phase Response Linearization of an All Pass Network System
Magnitude and Phase response of an All-Pass Crossover Loudspeaker System
Magnitude and Phase response of an All-Pass Crossover Loudspeaker System Compared to a model of a Minimum Phase System Minimum Phase Response
The Phase Shift at 1.4kHz could be approximated with a model of an All-Pass Filter Model of the 1.4kHz All-Pass Component Model of the 1.4kHz All-Pass Component
The 1.4 khz All-Pass Filter could be inverted via an FIR Inverse Filter Model of the 1.4kHz Inverted All-Pass Component
The result of the application of the inverse filter to approximate a Minimum Phase Response All-Pass Compensated Phase Response
Further improvement of the Minimum Phase Response approximation is possible improving The LF part of the inverse filter Non Minimum Phase-Shift at LF
Final Result of the Improved Phase Response Compensation with the inverse filter Added LF Phase Shift Compensation
Implementation of a Delay Compensated Crossover Type via Passive Filter
Passive Filter Delay Compensated System Total Magnitude, Single Contributions Magnitude and Phase Response Passive Filter + Input EQ Combination Phase Match around Crossover Region
Passive Filter Delay Compensated System STEP RESPONSE
Passive Filter Delay Compensated System Beamwidth, Directivity Index and Polar Maps of Both Planes
Thank You