|Designing A Limiter For Headphone Amplifiers|
(A HeadWize Design Paper)
When used with headphones - especially personal monitors, audio limiters (also called clippers) can help maintain safe listening levels. Without a limiter, large transients in audio signals could generate dangerous SPLs in headphones, although the average volume might be set at an acceptable level. Because the ambient noise on stage can be fairly high, performers are tempted to steadily increase the volume of their personal monitors in order to hear the mix. Limiters can ensure that headphone volume never exceeds a pre-determined threshold.
Because a limiter is actually a specialized form of audio compressor, the circuitry of audio limiters can vary tremendously in complexity from a pair of diodes to multi-stage voltage controlled amplifiers with split frequency bands. Diode-based limiters are instanteous, simpler in design and have a more accurate loudness response, but suffer from distortion in the clipping region. VCA-type limiters have low distortion, but can exhibit breathing or pumping effects from poor gain control. This article takes especial note of design principles for diode-based limiters and the wide range of clipping characteristics. For more information about limiters and compressors, see Signal Processing Fundamentals.
A diode has infinite resistance until the voltage across it is high enough to forward bias it (typically 0.7V for a silicon diode) at which point, current flows. The diode's voltage drop remains fairly constant throughout the operating range, and it is this property that is exploited in diode-based limiter circuits. Since audio signals are AC, two diodes together can symmetrically clip both the positive and negative halves of the waveform.
The output of a hard limiter has a maximum voltage that is the forward bias voltage of the diodes. Figure 1 shows the most basic of diode limiter circuits, a hard limiter. The design assumes that the input will exceed 1V. The trimmer pot P is adjusted for maximum volume from the headphone amplifier. Because the clipping can be abrupt and drastic, the distortion of a hard limiter in the clipping range is harsh (crackly) and is sometimes used for a fuzzbox-like effect. By scaling the resistors down, the hard limiter (and the soft limiter in figure 2) could drive some headphones directly.
The hard limiter can achieve an output with a slightly more dynamic characteristic with the addition of a resistor to form a voltage divider with R1. The soft limiter shown in figure 2 still clips a waveform above the forward bias voltage, but also lets through an amount (Vin - 0.7V)/10 by taking the output above R2. The graph in figure 3 compares the response of both types of limiters. The soft limiter is a type of compressor with a compression ratio determined by R1 and R2. Increasing R2 will give a more dynamic sound at the expense of level control.
The harsh characteristic of a hard limiter is partially due to the odd-order distortion harmonics that are generated during clipping. Jack Orman at the Analog Music Zone has analyzed diode clipping and has documented that germanium diodes (such as the 1N34A) have a smoother, tube-like clipping quality because they distort with more even-order harmonics, which are more pleasant to the human ear. Germanium diodes have a forward bias voltage of about 0.3V and are usually deployed 3 per side.
A pair of LEDs improves on silicon or germanium diodes as they clip with stronger even-order harmonics. Orman believes that a pair of one red and one green LED will sound better still, because the mismatching will highlight the even-order distortion. The limiter in figure 4 is an active design with the LED clippers in parallel with the feedback resistor of an opamp. The clipping threshold is about 1.9V, which is the forward bias voltage of an LED.
Figure 5 shows two limiter configurations based on zener diodes. The circuit in 5a clips when the input exceeds the breakdown voltage of one zener and the forward bias voltage of the other. The second limiter in figure 5b requires only one zener diode and clips when the input is greater than the breakdown voltage of the zener combined with the forward bias voltages of each diode pair. Zeners have the advantage of being easier to match for symmetric clipping than other types of diodes over a wide range of voltages.
The limiter circuits shown so far have fixed clipping levels (and are adapted to different headphone amplifiers by way of attenuators). One way to vary clipping levels is to apply a bias voltage to the normally grounded side of the diode array. The circuit in figure 6a permits manual adjustment of the positive and negative portions of the waveform separately. The variable clipper in figure 6b puts the audio signal through an inverting amplifier, the output of which connects to the bottom of the zener array. The limiter clips when the audio signal exceeds |(Vf + Vz) / (1 + (R2 * R5 / R3 * Rx))|, where Vf is the forward bias voltage of a zener and Vz is the breakdown voltage. R5 adjusts the feedback of the inverting amp and thus the clipping level.
Broadband limiters work across the entire frequency range. There are times when clipping should be frequency dependent. For example, if the audio signal is laced with noise, then clipping the high frequencies can result in smoother, more intelligible sound. The circuit in figure 7 is one example of a bandwidth restricted limiter. The low frequency clipping level of the diode array is modulated by the output of the low pass filter, so that only the high frequencies are affected.
Another way to configure a frequency dependent limiter is pre-emphasize the audio signal before the clipping stage. The analog tape compressor by LXH2 in figure 8 simulates the high frequency clipping distortion in analog tape recorders (useful in digital recording) by applying a 70 microsecond pre-emphasis (high frequencies above 2.4kHz) in the first stage network. After the clipping stage, the signal is de-emphasized in another network with the same corner frequencies. The diode array is a mix of silicon and germanium diodes to achieve the desired clipping characteristic.
When the audio signal is clipped, a limiter will generate harmonic and intermodulation distortion above and below the frequency of clipping. A multiband limiter (figure 9) minimizes these distortion components by splitting the audio signal into pre-determined frequency bands, each with their own clipping stage. The output of each clipping stage is then filtered for distortion outside the band before all bands are recombined into a single waveform.
In practice, multiband limiters are difficult to implement. Because the various filters of different orders will phase-shift the signals in each band, the overall response of a multiband limiter may not be flat and can sound unnatural. Several techniques can improve the performance of multiband limiters. First, the bands can be chosen according to psychoacoustic masking curves that help conceal distortion. Second, compressors can be introduced before the clipping stage to control the degree of clipping. Distortion detectors can control the amount of compression. Third, all-pass filters can be sprinkled about to collimate the phase responses of the bands.
On average, the bass frequencies in an audio signal usually have the highest amplitudes. When a low frequency signal of sufficient amplitude trips a limiter, high frequencies are also "pinched." The design in figure 10 is a multiband clipper that specializes in minimizing the harmonic and intermodulation distortions due to low frequency clipping only. The high and low pass filters split the audio signal with the low frequencies going through a variable clipper that is controlled by an intermodulation distortion detector. The second low pass filter after the variable clipper removes any harmonics caused by the clipping before summing the output with the high frequency band.
The IM detector estimates the amount of high frequency clipping in the fixed clipper resulting from low frequency clipping, and correspondingly decreases the threshold in the variable clipper to decrease the low frequency amplitude. The differencer recovers high frequency peaks, which determine the clipping level in the variable limiter. The peak detector enables the IM detector only when there are peak bass frequencies.
With any limiter, if the audio signal is conditioned with high frequency pre-emphasis (see the analog tape compressor above), then de-emphasis will reduce the high frequency distortion components due to clipping. The circuit in figure 11 cancels low frequency distortion. The audio signal pre- and post-clipping is compared in a differential amplifier and the output is put through a low pass filter to extract the low frequency distortion. Since the output of the low-pass filter is phase shifted, the clipped signal is delayed through an all-pass filter (assuming a minimum phase low-pass) to compensate and then differenced with the output of the low-pass filter. In a multiband limiter, the output of each band may have its own distortion cancellation circuit.
Chandler Jr., James, "Simple Projects," Electronic Musician, January 1990, p. 24.
Fukushima, Isao, "Limiter Circuit For Removing Noise From Demodulated Signals," U.S. Patent No. 4,256,975, March 17, 1981.
Orban, Robert, "Apparatus and Method for Peak-Limiting Audio Frequency Signals," U.S. Patent No. 4,208,548, June 17, 1980.
Orban, Robert, "Multiband Signal Processor," U.S. Patent No. 4,412,100, Oct. 25, 1983.
Schlesinger, Eugene, "Circuit Having Adjustable Clipping Level," U.S. Patent No. 4,138,612, Feb. 6, 1979.
Werrbach, Donn R., "Split-Band Limiter," U.S. Patent No. 5,737,432, April 7, 1998.
12/9/2007: Corrected figure 5b.