Tag: Mid-Side Recording

A microphone’s directional polar pattern is not generated by digital filtering or electronic EQ—it is a masterpiece of acoustic delay networks, phase cancellation, and dual-membrane voltage summation. Understanding the mathematical polar equations governing Omnidirectional, Cardioid, Supercardioid, Hypercardioid, and Figure-8 responses allows recording engineers to maximize signal-to-bleed isolation, control room reverberation ratios, and construct phase-coherent stereo microphone arrays.

In electro-acoustics, the directional sensitivity of any first-order microphone at an incident horizontal angle theta (where 0 degrees represents directly on-axis in front of the capsule) is described by the universal first-order polar equation:

Universal First-Order Polar Sensitivity Equation:
S(theta) = A + B * cos(theta)   (where A + B = 1)

Where:
- A          = Proportion of Omnidirectional (Pressure) sensitivity
- B          = Proportion of Bidirectional / Figure-8 (Pressure-Gradient) sensitivity
- theta      = Angle of acoustic incidence in degrees (0 deg = On-Axis Front, 180 deg = Rear)
- cos(theta) = Trigonometric cosine of the incidence angle

By adjusting the ratio of A (pressure) to B (pressure-gradient), five distinct directional patterns emerge:

• Omnidirectional (A = 1.0, B = 0.0): S(theta) = 1. Sensitivity is identical across all 360 degrees.
• Subcardioid / Wide Cardioid (A = 0.7, B = 0.3): S(theta) = 0.7 + 0.3 * cos(theta). Provides gentle -10 dB rear attenuation with minimal off-axis coloration.
• Cardioid (A = 0.5, B = 0.5): S(theta) = 0.5 + 0.5 * cos(theta). At 180 degrees rear incidence, cos(180) = -1, resulting in 0.5 + 0.5(-1) = 0 (complete theoretical cancellation directly behind the microphone).
• Supercardioid (A = 0.37, B = 0.63): Narrows the forward pickup beam and shifts the maximum cancellation nulls to 125 degrees and 235 degrees, introducing a small rear lobe of opposite polarity.
• Hypercardioid (A = 0.25, B = 0.75): Maximizes random-energy efficiency (maximum rejection of diffuse room reverb), placing deep cancellation nulls at 110 degrees and 250 degrees with a -6 dB rear lobe.
• Bidirectional / Figure-8 (A = 0.0, B = 1.0): S(theta) = cos(theta). Equal sensitivity at 0 degrees (positive polarity) and 180 degrees (negative polarity), with dead-zone nulls at 90 degrees and 270 degrees.

How does a single-diaphragm cardioid microphone achieve rear cancellation? Engineers design an Acoustic Delay Labyrinth inside the capsule housing:

Rear entry ports are machined into the sides of the capsule cylinder, leading through internal porous damping meshes and acoustic chambers to the back of the diaphragm. The internal acoustic resistance and compliance are tuned so that the internal travel time tau_internal exactly matches the external propagation time tau_external for a sound wave traveling from the rear port to the front of the membrane:

• Sound Arriving from 180 Degrees (Rear): The wave enters the rear port and travels through the internal labyrinth, arriving at the back of the diaphragm at the exact same microsecond that the external wave wraps around to the front of the diaphragm. Equal pressure on both sides yields zero net movement!
• Sound Arriving from 0 Degrees (Front): The wave strikes the front of the diaphragm first, then travels around to the rear port and through the internal delay network, arriving at the rear surface delayed in phase. This phase differential reinforces forward diaphragm excursion.

Multi-pattern studio condensers (like the Neumann U87 or AKG C414) mount two cardioid capsules back-to-back sharing a central brass backplate. By varying the DC polarization voltage on the rear membrane while holding the front membrane at +60V DC:

1. Rear Membrane at 0V (Disconnected): Only the front cardioid element is active -> Cardioid Pattern.
2. Rear Membrane at +60V (In Phase with Front): Front Cardioid + Rear Cardioid = Omnidirectional Pattern.
3. Rear Membrane at -60V (Out of Phase with Front): Front Cardioid – Rear Cardioid = Bidirectional (Figure-8) Pattern.

Every directional (pressure-gradient) microphone exhibits the Proximity Effect: a pronounced boost in low-frequency response below 300 Hz when the sound source moves within 30 centimeters of the capsule.

This occurs because acoustic waves radiate spherically from a point source, and sound pressure decays inversely with distance (1/r). At long distances (far-field), wavefronts are essentially flat plane waves, and the amplitude difference between the front and rear of the capsule is negligible compared to the phase difference. However, at close distances (near-field, where r is small relative to low-frequency wavelengths), the inverse-distance pressure drop across the capsule thickness becomes significant, adding a massive amplitude gradient on top of the phase gradient at low frequencies!

• Pure Figure-8 Microphones: Exhibit the strongest proximity effect because they operate as 100% pressure-gradient devices.
• Cardioid Microphones: Exhibit moderate proximity effect (50% pressure-gradient).
• Pure Omnidirectional Microphones: Exhibit zero proximity effect, allowing a vocalist or acoustic bass to be miked 1 inch from the grille without any low-frequency boominess.

The following reference table details the mathematical and acoustic parameters of standard studio polar patterns:

When two or more microphones capture the same acoustic source at different physical distances, the signal arrives at the further microphone delayed by time Delta_t = Delta_d / c (where c is the speed of sound, approximately 343 meters/second at 20°C).

When these two microphone channels are summed together in a mixing console, constructive and destructive interference creates Comb Filtering—a series of deep, periodic phase cancellation notches across the frequency spectrum:

Acoustic Comb Filter Cancellation Formula:
First Cancellation Null:    f_0 = 1 / (2 * Delta_t) = c / (2 * Delta_d)
Subsequent Nulls:           f_n = (2n + 1) * f_0    (for n = 1, 2, 3...)

Example: Path length difference Delta_d = 17.15 cm (0.1715 meters)
Delay Delta_t = 0.1715 / 343 = 0.0005 seconds (0.5 ms)
First Phase Null f_0 = 1 / (2 * 0.0005) = 1,000 Hz (-Infinity dB cancellation if equal amplitude!)
Subsequent Nulls at: 3,000 Hz, 5,000 Hz, 7,000 Hz, 9,000 Hz...

To prevent audible comb filtering when miking multiple sources or using multiple mics on an ensemble, engineers enforce the 3:1 Rule: the distance between any two microphones must be at least three times the distance from each microphone to its primary sound source. Due to the Inverse Square Law, a 3:1 distance ratio attenuates the off-axis bleed by at least 9.5 dB, limiting comb filter ripples to less than +/- 1 dB when summed to mono.

Human binaural hearing localizes stereo imaging using two psychoacoustic cues: Interaural Level Differences (ILD) (amplitude variations above 1.5 kHz caused by head shadowing) and Interaural Time Differences (ITD) (phase arrival delays below 800 Hz between the left and right ears). Studio stereo arrays exploit these mechanisms across three geometric categories:

• 1. Coincident Arrays (Pure ILD / 100% Mono-Compatible):
  • XY Pair: Two cardioid capsules mounted with their diaphragms vertically aligned at the exact same point in space, angled between 90° and 135°. Because path distances are identical, there is zero phase difference when summed to mono.
  • Blumlein Pair: Invented by Alan Blumlein in 1931, using two crossed Figure-8 microphones angled at 90°. Delivers extraordinary stereo realism and natural room ambience.
  • Mid-Side (M-S) Array: Pairs a forward-facing Mid capsule (Cardioid or Omni) with a perpendicular Side Figure-8 capsule facing left/right. Decoded via a sum-and-difference matrix (Left = Mid + Side, Right = Mid - Side), allowing the engineer to adjust stereo width dynamically during mixing while guaranteeing 100% mono compatibility (Left + Right = 2 * Mid).
• 2. Near-Coincident Arrays (Hybrid ILD + ITD):
  • ORTF (Office de Radiodiffusion Télévision Française): Two cardioid capsules spaced 17 cm apart (matching human ear spacing) and angled outward at 110°.
  • NOS (Nederlandse Omroep Stichting): Two cardioid capsules spaced 30 cm apart and angled at 90°.
• 3. Spaced Arrays (Pure ITD):
  • A-B Spaced Omnis: Two omnidirectional pressure microphones spaced 40 cm to 3 meters apart. Captures expansive low-frequency spaciousness and concert hall envelopment.
  • Decca Tree: Developed by Decca Records engineers for orchestral scoring, consisting of three omnidirectional microphones (traditionally Neumann M50s) arranged in a forward-pointing T-triangle (2 meters left-to-right spacing, with the center mic advanced 1.5 meters forward).

For specialized film production and architectural capture, engineers extend first-order polar mechanics using physical wave manipulation:

• Shotgun (Lobar) Interference Tubes: Mounts a slotted metallic tube in front of a hypercardioid capsule. Sound arriving from the sides enters the tube slots at staggered distances, arriving at the diaphragm out of phase and canceling out above 1.5 kHz, creating a narrow forward beam for booming film dialogue.
• Boundary / Pressure Zone Microphones (PZM): Mounts a miniature capsule flush with a large reflective boundary plate (or floor/wall surface) with a microscopic 1mm gap. Direct and reflected waves arrive at the capsule in exact phase coherence, eliminating floor-bounce comb filtering and providing a hemispherical +6 dB sensitivity boost.

Mastering polar geometry and acoustic phase relationships transforms microphone placement from guesswork into deterministic science:

• Select Cardioid and Supercardioid patterns to isolate individual instruments in dense ensemble tracking or untreated environments, carefully aligning null angles (180° for Cardioid, 125° for Supercardioid) directly toward the loudest bleed source.
• Exploit the 90° Nulls of Figure-8 Microphones to record simultaneous singing guitarists (angling the vocal mic’s 90° null at the guitar and the guitar mic’s 90° null at the mouth).
• Use Coincident XY or Mid-Side Arrays when broadcast mono-compatibility and pinpoint stereo localization are non-negotiable.
• Deploy ORTF or Spaced Omnidirectional Arrays when capturing acoustic ensembles in world-class reverberant halls where low-frequency extension and spacious envelopment are desired.