Click here to purchase the entire book in PDF format. Pressure Gradient Transducers The behaviour of a Pressure Gradient transducer is somewhat different because the incoming pressure wave reaches both sides of the diaphragm. Remember that the lower the frequency, the longer the wavelength. Also, consider that, if a sound source is on-axis to the transducer, then there is a path length difference between the pressure wave hitting the front and the rear of the diaphragm. That path length difference remains at a constant delay time regardless of frequency, therefore, the lower the frequency the more alike the pressures at the front and rear of the diaphragm because the phase difference is smaller with lower frequencies. The delay is constant and short because the diaphragm is typically small. Figure 6.115: A diagram of a Pressure Gradient transducer showing the two paths to the front and rear of the diaphragm from a source on axis. Since the sensitivity at the rear of the diaphragm has a negative polarity and the front has a positive polarity, then the result is that the pressure at the rear is subtracted from the front. With this in mind, let's start at a frequency of 0 Hz and work our way upwards. At 0 Hz, then the pressure at the rear of the diaphragm equals the pressure at the front, therefore the diaphragm does not move and there is no output. (Note that, right away, we're looking at a different beast than the perfect Pressure transducer. Without the capillary tube, the pressure transducer would give us an output with a 0 Hz pressure applied to it.) As we increase in frequency, the phase difference in the pressure wave at the front and rear of the diaphragm increases. Therefore, there is less and less cancellation at the diaphragm and we get more and more output. In fact, we get a doubling of output for every doubling of frequency - in other words, we have a slope of +6 dB per octave. Eventually, we get to a frequency where the pressure at the rear of the microphone is 180$^{\circ }$ later than the pressure at the front. Therefore, if the pressure at the front of the microphone is high and pushing the diaphragm in, then the pressure at the rear is low and pulling the diaphragm in. At this frequency, we have constructive interference and an increased output by 6 dB. If we increase the frequency further, then the phase difference between the front and rear increases and we start approaching a delay of 360$^{\circ }$. At that frequency (which will be twice the frequency where we had +6 dB output) we will have no output at all - therefore a level of $-\infty$ dB. As the frequency increases, we result in a common pattern of peaks and valleys shown in Figure 6.116. Figure 6.116: A linear plot of a comb filter caused by the interference of the pressures at the front and rear of a Pressure Gradient transducer. The harmonic relationship between the peaks and dips in the frequency response is evident in this plot. Figure 6.117: A semi-logarithmic plot of a comb filter caused by the interference of the pressures at the front and rear of a Pressure Gradient transducer. The 6 dB/octave rise in the response up to the lowest-frequency peak is evident in this plot. The frequencies of the peaks and valleys in the frequency response are determined by the distance between the front and the rear of the diaphragm. This distance, in turn, is principally determined by the diameter of the diaphragm. The smaller the diameter, the shorter the delay and the higher the frequency of the lowest-frequency peak. Most manufacturers build their bidirectional microphones so that the lowest frequency peak in the frequency response is higher than the range of normal audio. Therefore, the ``standard'' frequency response of a bidirectional microphone starts an output of 0 at 0 Hz and doubles for every doubling of frequency to a maximum output that is somewhere around or above 20 kHz. Figure 6.118: The output of a Pressure Gradient transducer whose design ensures that the entire audio range lies below the lowest-frequency peak in the frequency response. This, of course, is a problem. We don't want a microphone that has a rising frequency response, so we have to fix it. How? Well, we just build the diaphragm so that it has a natural resonance down in the low frequency range. This means that, if you thump the diaphragm like a drum head, it will ring at a very low note. The higher the frequency, the further you get from the peak of the resonance. This resonance acts like a filter that has a gain that increases by 6 dB for every halving of frequency. Therefore, the lower the frequency, the higher the gain. This counteracts the rising natural slope of the diaphragm's output and produces a theoretically flat frequency response. The only problem with this is that, at very low frequencies, there is almost no output to speak of, so we have to have enormous gain and the resulting output is basically nothing but noise. Figure 6.119: The blue plot shows the gain response of a theoretical filter required to ``fix'' the frequency response of the transducer shown in Figure 6.118. Note the extremely high gain required in the low frequency range. The red plot shows the gain achieved by making the diaphragm naturally resonant at a low frequency. Note that there is a bottom limit to the benefits of the resonance. Figure 6.120: The blue plot shows the result of the frequency response of the output of the transducer shown in Figure 6.118 filtered using the theoretical (blue) gain response plotted in Figure 6.119. Note that this is a theoretical result that does not take real life into account... The red plot shows a more likely scenario where the extra gain provided by the resonance doesn't extend all the way down to 0 Hz. The moral of this story is that Pressure Gradient microphones have no very-low-frequency output. Also, keep in mind that any microphone with a Pressure Gradient component will have a similar response. Therefore, if you want to record program material with very-low-frequency content, you have to stick with omnidirectional microphones.