Implementation of a virtual analog phaser based on the MXR phase 100 guitar pedal.

1. VIRTUAL ANALOG PHASERS
Ricardo Falcón Pérez
Aleksi Myöhänen

2. BRIEF HISTORY OF PHASERS
Famous users
• Rush
• Pink Floyd
• Eddie Van Halen
Introduced in the 1970s

3. ALLPASS FILTER
• Magnitude response is flat
• Phase response is not trivial
• Cascade of N filters introduces a maximum phase
shift of –Nπ radians
A 𝑧 =
𝑎1+𝑧−1
1+𝑎1 𝑧−1
ASP Course: Slides for Lecture 2
R.Kiiski et al., Time-variant gray-box modelling
of a phaser pedal

4. PHASER
• A case with 4 AP filters and no
feedback (MXR Phase 90)
• All filters share the same
coefficient
• 1 notch for every 2 filters
R.Kiiski et al., Time-variant gray-box
modelling of a phaser pedal
Julius Smith and Nelson Lee, 2008, Time Varying Delay Effects

5. PHASER
Magnitude response of the
phaser with 4 AP filters

6. PHASER WITH FEEDBACK
• Feedback can be added at any stage of the system (*)
• Feedback case can be solved explicitly or implicitly
• Feedback can be positive or negative
R.Kiiski et al., Time-variant gray-box modelling
of a phaser pedal

7. PHASER WITH FEEDBACK
Magnitude response with 10 filters with no feedback Effect of feedback on the magnitude response

8. IMPLEMENTATION
• Roughly based on the MXR Phase 100 pedal
• 10 all pass filters
• AP-Filters 1,2, 9, 10 have a fixed coefficient
• AP-Filters 3, 4, …, 8 have a modulated coefficient
• Range for the coefficient a0 = [-0.84, -0.4]
• Break frequency ≈ [1100 Hz, 4200]
• LFO with a triangular shape
• Feedback from output of filter 6, to input of filter 2
• Includes a DC blocker (high pass filter)
• Includes saturation stage

9. IMPLEMENTATION

10. IMPLEMENTATION
Magnitude response of our Phaser

11. SOUND EXAMPLES
No Phaser Phaser 4 AP filters
Phaser 10 AP filters, No
Feedback
Fb = 0
LFO = 0.8 Hz
A0 = [-0.84, -0.4]
Phaser 10 AP filters,
Hi neg Feedback
Fb = -0.85
LFO = 0.8 Hz
A0 = [-0.84, -0.4]
Phaser 10 AP filters,
Low positive Feedback
Fb = 0.3
LFO = 0.8
A0 = [-0.84, -0.4]
Phaser 10 AP filters, Low
positive Feedback,
saturation
Fb = 0.3
LFO = 0.8
A0 = [-0.84, -0.4]
SatGain = 6 dB
Clean Guitar – Chords with open strings

12. SOUND EXAMPLES
Phaser 10 AP filters
After distortion
FB = 0.2
LFO = 0.6
A0 = [-0.84, -0.4]
Phaser 10 AP filters Before
distortion
FB = 0.2
LFO = 0.6
A0 = [-0.84, -0.4]
Distorted Guitar – Busy riff
Full drum kit – Funky groove
No phaser Phaser 10 AP filters
FB = 0.3
LFO = 0.6
A0 = [-0.84, -0.4]

13. CONCLUSIONS
• Highly customizable
• Feedback makes notches less deep but introduces resonance
• 10 filters implementation attenuates low frequencies more than 4 filters

14. REFERENCES
• Roope Kiiski, Fabian Esqueda and Vesa Välimäki, 2016, “Time-variant gray-box
modelling of a phaser pedal”
• Julius Smith and Nelson Lee, 2008, “ Time Varying Delay Effects”
• Photo of the MXR phase 100 http://www.dynasite.net/dynaweb/1001081/MXR-M-
107-Phase-100-Phaser-Pedal.htm
• http://rush.wikia.com/wiki/Alex_Lifeson_equipment
• http://www.gilmourish.com/?page_id=20
• https://fi.pinterest.com/gclyn/rush/