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Assessing The Impact: The Effect Of Cupping On Cardioid Microphone Directivity

Investigating by measuring polar plots, directivity index, relative frequency responses at different angles and the change in frequency response.
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Sound engineers are generally well aware that when a microphone of the cardioid family (just cardioid, or else subcardioid, hypercardioid or supercardioid) is “cupped,” its unidirectional polar pattern tends to become omnidirectional, which, aside from changes in the frequency response, means reduced gain before feedback. Not exactly a minor issue in sound reinforcement.

The reason for this behavior is that the design of the cardioid family of microphones combines the pickup from the front of the diaphragm with the contribution of a rear port to obtain directionality, so by blocking the rear of the grille we obstruct the access of sound to the rear port and therefore lose some of the directivity of the capsule.

I wanted to check to what extent this is the case. Because I run a loudspeaker measurement service, I’m used to rotating a loudspeaker and measuring it with a fixed mic inside an anechoic chamber, so it was just a question of rotating the mic instead and keeping the loudspeaker fixed to obtain high-resolution frequency responses at different angles from which different graphical representations could be calculated: polar plots, directivity index, relative frequency responses at different angles and the change in frequency response with respect to the original mic.

In its most radical form, cupping (the way in which a mic is held by placing one or two cupped hands over the grille mesh) exposes only the front of the grille, with devastating effects on frequency response. In this case I just wanted to see the effect on directivity, so I used relatively light cupping, which was simulated by taping the back of the grille from the ring to the body. The mic used in the experiment was that cardioid vocal microphone designed in the 1960s that is well known to everyone.

A number of graphical representations to understand the changes produced are included here. When results for both conditions share a figure, the untreated mic is shown in green while the line for the cupped one is red.

POLAR PLOTS
First, we see the polar curves corresponding to the 500, 1000, 2000 and 4000 Hz octave bands (Figure 1). In all cases it can be seen that the polar response of the taped version (in red), although not completely omnidirectional, is much less directive than when the grille is left unobstructed.

Figure 1: Polar plots. Although this iconic mic is nominally cardioid, it’s actually halfway between a cardioid and a supercardioid, hence the absence of the notch on the back of a heart-shaped polar curve.

DIRECTIVITY INDEX
In Figure 2, the directivity index is shown with respect to frequency (on the right side of the graph we have noted the equivalence with the directivity factor Q). A theoretically perfect cardioid family mic
at all frequencies would show a straight line. The curves show a substantially higher directivity for the measurement with the unblocked grille (in green) up to 5 kHz.

Figure 2: Directivity index.

Both can also be seen becoming omnidirectional at frequencies above 13 kHz. As a reference comparison for Di, a loudspeaker with a 4-inch cone would exhibit similar directivity around 1 kHz to our uncupped mic.

RELATIVE FREQUENCY RESPONSES
Figure 3 shows the difference in frequency response for 0 (front), 45, 90, 135 and 180 degrees (back) so you can see how the shape of the frequency response changes at different angles when the back is obstructed. Since these are responses relative to 0 degrees, the 0-degree response is the straight blue dotted line at 0 dB.

Figure 3: Relative frequency responses for 0, 45, 90, 135 and 180 degrees.

For a perfectly cardioid family mic at all frequencies, we would see perfectly straight lines at different levels. In the case of the uncupped microphone (top plot), it can be seen that the responses at different angles are somewhat irregular; this half-a-century-old design shows its age (but remains a popular piece nonetheless).

A good current design would show smoother more consistent curves that remain more or less flat for different angles. In contrast, the responses of the obstructed capsule are smoother (since the pickup is mainly from the front of the diaphragm), although at the expense of high frequency roll off, as well the loss of rear attenuation.

PICKUP (ACCEPTANCE) ANGLE
Figure 4 shows the pickup angle for both measurements, calculated for an attenuation level of -6 dB (usually the -3 dB angle is used, but the wider angle here makes the change of angle with frequency more visually obvious across a wider band.

Figure 4: Pickup angle (-6 dB).

As a reference for what one should expect, a microphone of the cardioid family would show the same angle at all frequencies, like a constant directivity horn. The green curve, which corresponds to an unobstructed grille, has a smaller angle (since the directivity is higher) and a flatter curve.

CHANGE IN FREQUENCY RESPONSE
In this last curve (Figure 5) we see the relative changes to the (on-axis) frequency response. Positive values mean more pickup level for the uncupped mic.

Figure 5: Change in frequency response. Parameters with frequency were calculated at high resolution (24 points per octave) and then 1/3rd-octave smoothed for clarity.

On the one hand, it is evident that even the light cupping we used for the experiment, that left the sides unobstructed, substantially changes the frequency response.

On the other hand, the level picked up is higher in the unobstructed measurement, something that could be expected as the pickup becomes wider when the back port is obstructed (just like a narrower horn will provide more sound pressure on-axis).

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