HomeHow Linear is Fender Optical "Vibrato" (Really Tremolo)?

Introduction. The previous article, "A Closer Look at Fender Optical 'Vibrato' (Really Tremolo)", focused mainly on the low-frequency oscillator (LFO), neon lamp and driver characteristics, and response speed of the light-dependent resistor (LDR; photocell). The tremolo modulation waveform was investigated using a DC supply and a resistive source impedance of 38 K ohm, instead of using an AC signal and a vacuum triode source. However, examining audio performance obviously requires an AC test signal. And vacuum tube non-linearity probably has a role in the effect's "character" or "warmth;" possibly, photocell non-linearity also contributes. The goal of this follow-up article is to examine sources of harmonic distortion in the vintage Fender optical tremolo system.

A schematic diagram and description of the low-frequency oscillator (LFO) and neon lamp driver is given in the previous article. In the optical coupler, neon lamp pulses transiently lower the resistance of the LDR. In parallel with the intensity control, the LDR forms the shunt resistance of a ground-referred voltage divider (or "L-pad"); the series resistance is the source impedance of the audio path's preceding triode stage, which is close to 38 K ohm. As LDR resistance decreases, the signal voltage dropped across this source impedance increases, effectively reducing that stage's gain. Thus the amplitude at the input of the following stage (the power amplifier's polarity splitter) decreases with each neon lamp pulse, amplitude-modulating the signal. How does harmonic distortion change when the triode is loaded by the LDR in its different states?

The LDR-Loaded Triode Circuit is Apparently the Same in All Fender Amps with Optical Tremolo. I studied the set of 33 vintage Fender amplifier schematics used in the previous article, which are listed here by their LFO/neon driver circuit category. All of these have the same LDR-loaded triode cicuit feeding the power amp. This circuit is given below, in Figure 1.

Figure 1: Schematic of triode circuit loaded by LDR in vintage Fender amps with optical tremolo.

Figure 1. Schematic diagram of the triode circuit loaded by the LDR/"vibrato" intensity control network in vintage Fender amp models equipped with optical tremolo. This circuit is common to all 33 schematics examined. The average B+ power supply voltage (+354 VDC) was calculated from values reported for all but one of these (a preamp-stage B+ voltage was not given for "Deluxe Reverb-Amp AB868"). Numbered components (e.g., C1, R2) refer to this Figure only, and are not keyed to other drawings in my web pages or in the vintage schematic set.

The tremolo network-loaded stage uses one triode of a 7025 twin triode. As far as I know, the 7025 is functionally equivalent to the 12AX7. Therefore I am uncertain why all of the vintage schematics call for a 7025 here (as well as in all preamp stages), while the same schematics specify a 12AX7 as the LFO/lamp driver tube. The Fender company must have believed there was a difference, otherwise one would expect simpler and cheaper equivalent results by specifying just one type of high-mu twin triode everywhere it was needed. Many players use the 12AX7 and 7025 interchangeably in these amps, and typically favor a specific tube brand more than seeking out one or the other type number. As described below, I used a vintage USA-made RCA 12AX7 in my experiments.

As shown in Figure 1, the cathode of the tremolo-loaded triode (at right) is linked to a second triode's cathode (at left), the two units sharing a common 820-ohm cathode bias resistor (R3) bypassed with electrolytic capacitor C1. This bypass capacitor makes the two triodes essentially independent at audio frequencies, and they have the same DC operating point (quiescent plate current) since their plate load resistors (R1 and R2) are equal (each is 100K ohm).Whether these two triodes are in the same tube or separate tubes depends on amplifier model: In models with reverb, the left triode amplifies the reverb tank's output, and the right triode mixes this reverb signal with the "Vibrato" channel's "dry" signal; in this case the two triodes use the same tube. In models without reverb, the two triodes are simply the second (and final) preamp stage (i.e., the tone and volume control follower) of the "Normal" channel (at left) or the "Vibrato" channel (at right); in this case the cathode-linked triodes are in separate tubes (one for each preamp channel), with co-enveloped triodes serving as first- and second-stage amplifiers per channel (as in all models).

The audio signal on the plate of the right-hand triode in Figure 1 AC-couples to the optical isolator's LDR and the "vibrato" intensity control via 100-nF capacitor C2. From there, via 220-K-ohm resistor R5, it passes to the "phase" inverter stage of the power amplifier (more accurately called a polarity splitter; see this link for my rant about the difference between polarity and phase). The corresponding series resistor for the "Normal" channel (R4) lets the power amp front-end double as a mixer (summing amplifier) for the two channels; that stage's high input impedance and the relatively large values of R4 and R5 effectively isolate the two channels, preventing the tremolo network from modulating the "Normal" channel.

Interestingly, the coupling capacitor analogous to C2 for the "Normal" channel (not drawn in Figure 1) is always specified as 47 nF, or half the value of C2. Because the "Vibrato" channel needs to operate into a lower load resistance (50 K ohm maximum) compared to the "Normal" channel, the designers probably chose the higher C2 value to minimize low-frequency loss in the "Vibrato" channel. How is low-frequency response affected during tremolo attenuation phases, when LDR illumination results in load resistances below 50 K? That is, what higher frequency does the high-pass corner frequency (Fc; the frequency for -3dB loss) reach at maximum tremolo attenuation? The well-known equation Fc = 1/(2piRLC), where RL is the load resistance and C is the coupling capacitor value, assumes zero source impedance and gives the wrong answer if applied here. Accounting for source impedance (RS), the correct equation is Fc = 1/(2pi[RS+RL]C). Plugging in RS = 38 K and C = 100 nF, the 50-K maximum load value gives a corner frequency of 18.1 Hz. With a 3-K load, this rises to only 38.8 Hz, apparoaching as a limit 41.9 Hz at RL = 0 (dead short; gain also zero). Thus, the Fender optical tremolo design cannot erode the guitar-relevant bandwidth (whose low end is the E2 pitch, 82.407 Hz).

Operating Point and Load Lines. One can predict major aspects of a tube stage's performance, including gain and distortion, using the tube's published plate charateristic chart. Figure 2 shows RCA's "Average Plate Characteristics" for the 12AX7A, on which I plotted load lines relevant to the tremolo-loaded triode stage. The inset diagrams this triode configured for the average operating point used in Fender amps. For simplicity, it shows a 1640-ohm cathode bias resistor serving a single triode. This is equivalent to (drops the same voltage as) a 820-ohm resistor serving two triodes that have equal plate load resistors. Setting B+ at 350 V and using a 100-K-ohm plate load resistor defines the DC load line drawn in blue. Its slope is the negative reciprocal of 100 K and its voltage-axis intercept is 350 V. I will spare you the details of how plate characteristics are used to predict the performance of a given circuit; readers needing a review can easily find it elsewhere on the web. The main point of Figure 2 is to convey a sense of how optical tremolo-relevant loads map to the 12AX7's non-linearity.

Figure 2: 12AX7 plate characteristic chart overlayed with load lines relevant to Fender optical tremolo.
Figure 2. Plate characteristic chart of a 12AX7 triode overlayed with load lines plotted in color. Inset shows the relevant circuit. The DC load line is blue, and the operating point is indicated in purple. AC load lines correspond to a 50-K-ohm (green) or a 3.6-K-ohm (red) resistance shunting the output of the coupling capacitor to ground.

With a +350 V supply voltage, the cathode bias resistor fixes the operating point at 1.14 mA DC plate current, making the plate +238V and the cathode about +1.85V. Audio signals (AC) "see" the AC load resistor as in-parallel with the plate load resistor, since the impedance of the power supply and reactance of the coupling capacitor are each nearly zero ohms at audio frequencies. The slope of an AC load line is thus the negative recirocal of the paralleled "AC load R" and 100 K ohm, and the line is constrained to pass through the operating point. Figure 2 shows AC load lines for two tremolo-relevant AC load values: 50 K ohm (green), for maximum LDR resistance (dark phase) in parallel with the 50-K intensity pot, and 3.6 K ohm (red) for something close to minimum LDR resistance (maximum illumination) in parallel with a full-clockwise intensity pot (I chose 3.6 K because this is the approximate peak load with the AES replacement optical isolater in dynamic tests; see below).

Using a graphical approach, I obtained 40-K-ohm output impedance for the triode stage, and 30 dB gain for operation into a 50-K AC load (as reported below, these are very close to the values I measured empirically). Gain when the AC load is 3.6 K is more difficult to estimate graphically, due to the steep load-line slope. The 12AX7 circuit calculator at http://amps.zugster.net/tools/triode-calculator gives 13 dB in that case (also close to my empirical result). Although possible, accurate distortion predictions are cumbersome to calculate graphically, especially with a steep load line, so I relied on empirical measurements (see below). Qualitatively, however, since linearity is related to where a load line intersects the set of plate characteristic curves, it's easy to see from Figure 2 that load line slope should have some effect. Note that characteristic curves for an ideal (linear) triode would be perfectly equally spaced and parallel everywhere, unlike a real tube. I breadboarded a 12AX7 to measure distortion versus load, as described next.

Setup to Measure Characteristics of Optical Tremolo-Loaded Triode Circuit. I breadboarded essentially the same circuit as shown in Figure 1 and set the plate voltage at 350 V. Figure 3 diagrams the setup, instruments, experimental loads, and test points. Static tests used fixed resistors as loads (RLOAD), with gain and distortion at 1.0 KHz measured on a Hewlett-Packard 331A distortion analyzer. An oscilloscope monitored the distortion residue (waveform after eliminating the 1-KHz fundamental) at the analyzer's output. For actual vibrato conditions, dynamic tests used a replacement optocoupler, which was purchased from Antique Electronics Supply (AES), driven by my LFO/lamp driver breadboard; these are described in the previous article. Preliminary tests measured the triode circuit's output impedance as 38 K. As an experimental control to isolate non-linearity due to the LDR, some dynamic tests used a 38-K-ohm fixed resistor as source impedance. Audio recording for the dynamic experiments employed a Behringer UCA222 interface, whose 1.0-KHz analog input impedance measured 12.2 K-ohm in preliminary tests. As shown in Figure 3, this 12.2-K impedance was built out to 50 K using a series 37.7-K resistance; in parallel with the LDR of the optocoupler, this network is equivalent to the impedance of Fender's vibrato intensity pot at full clockwise.

Figure 3: Schematic diagram of experiments to measure non-linearity of Fender optical vibrato.

Figure 3. Schematic diagram of setup to analyze gain and distortion in Fender optical tremolo. The tube was wired as in Figure 1, and its non-used (left) triode was powered but not connected to any signal. The switch symbols illustrate how the signal path was configured for various tests; clip leads or soldering/desoldering implemented equivalent connections rather than physical switches. The LFO/lamp driver breadboard and AES replacement optical coupler were described in the previous article.

Photographs of the breadboards for the triode experiments are presented in Figure 4. In the loaded triode stage under test, I used a vintage USA-made RCA 12AX7 from the 1960s. In preliminary measurements, the operating point and gain of each of its triodes matched predictions (within 5 percent) from published tube characteristics (see Figure 2). Out of view in Figure 4 are most of the test instruments; I measured the total harmonic distortion (plus noise) of the direct 1-KHz output of the GW-Instek GAG-810 audio generator as 0.015 percent (-76.5 dB; slightly better than its specified maximum of 0.02 percent), and the residue was mainly second harmonic (data not shown). I decided this should be a sufficiently low-distortion signal source for these experiments and proceeded with static tests on the triode circuit, discussed next.

Figure 4: Photos of breadboards used to analyze distortion in Fender optical tremolo

Figure 4. Photos of breadboards configured for dynamic tests. The left photo includes (1) Behringer UCA222 interface, (2) LFO/neon lamp driver breadboard, (3) optical coupler, and (4) breadboard for the loaded triode circuit under test. The right photo is a closer view of (3) and (4).

Static Load Test on Triode Circuit. Figure 5 shows distortion measurements versus output amplitude of the triode stage as loaded by either 50 K ohm or 3.6 K fixed resistances. These RLOAD values, which match those given as examples in Figure 2, were chosen for their equivalence to actual tremolo conditions. The circuit is loaded at essentially 50 K (the value of the intensity control; see Figure 1) when the LDR is in its high-resistance, non-illuminated state. With the AES replacement optocoupler used in the dynamic tests (below), my previous results (see Figure 8 and Figure 11 in earlier article and associated discussion) indicated that, during tremolo, the minimum resistance of this unit's LDR was about 3.9 K ohm; thus 3.6 K represents this resistance in parallel with a full-clockwise intensity pot.

Figure 5: Static (fixed load) results on triode stage

Figure 5. Static (fixed load) results for the triode circuit given in Figure 3 working into RLOAD of either 50 K ohms (green curve) or 3.6 K (red). At 1.0 KHz, triode stage gain measured 30.3 dB or 13.8 dB, respectively, under these load conditions (note that these are the same two "AC loads" as featured in Figure 2). In the graph of distortion versus output amplitude (EOUT), the small circles are the measured data-points, and these are linked by smooth curves for each fixed load resistance. The dashed black lines link points on the two different curves that obtain at three example fixed input amplitudes (EIN). (One may choose any point on the 50-K load curve, go left horizontally by the difference in gain [16.5 dB], and then the vertical distance to the 3.6-K load curve is the increase in distortion as the load switches from 50 K to 3.6 K ohms.) The middle example coincides with the dynamic tests (below), which used -20.8 dBV input amplitude. The oscilloscope display on the right shows the distortion residue when the circuit was loaded at 3.6 K and EIN was -20.8 dBV; the substantially pure second-harmonic distortion, and its phase relationship to the fundamental, is typical of all points within the graph's area.

Comparing the two test loads, the difference in triode stage gain was 16.5 dB. Distortion increases with output amplitude in each case, as Figure 5 shows. If input amplitude is held constant, decreasing the load resistance increases the relative amount of distortion in the output; the magnitude of this increase depends on the given amplitude (it is small for small signals). As shown in the example oscilloscope display on the right in Figure 5, the distortion is mainly second harmonic (2 KHz in this case), typical of class-A vacuum triode amplifier stages operating below saturation. Note in the 'scope photo the phase relation between the second harmonic residue and the overall EOUT signal: The positive and negative maxima of EOUT each align with negative maxima of the distortion product. This means that positive output half-cycles tend to be "squashed" and negative ones "peaked." This is due to the relative crowding of the triode's plate characteristic curves in the low plate-current range (see Figure 2). The corresponding instantaneous plate voltage, as constrained by the load line, is thus "squashed" for positive output excursions.

As a bridge to the dynamic experiment (presented next), where EOUT (see Figure 3) was set at 3.0 VRMS (9.5 dBV) for the dark-state optocoupler, the input amplitude was -20.8 dBV; this corresponds to the middle of the three fixed-input examples drawn as dashed black lines linking the two distortion curves in Figure 5. There, switching the load from 50 K ohms to 3.6 K causes second harmonic distortion to increase from about 0.85 to 1.85 percent, or from -41.4 dB to -34.7 dB, respectively. This predicts something approaching 6.7 dB relative increase in second-harmonic amplitude at maximum LDR illumination in the dynamic experiment.

Dynamic Test Results. My dynamic experiments used a 1.0-KHz test signal, via either the relevant triode stage or a 38-K resistor, modulated by a Fender optical vibrato circuit (see Figure 3). The LFO breadboard was configured as circuit "Category 1" (see previous article) and set for minimum frequency (about 3.5 Hz). With the LFO off and the neon lamp dark, test signal amplitude was set such that 3.0 VRMS appeared at the EOUT test point (Figure 3); this placed 733 mVRMS (-2.7 dBV) across the input of the Behringer UCA222 interface (its maximum is +2.0 dBV). This is a 16-bit digital interface sampling at 44.1 KHz; I used only the left channel and recorded mono WAVE files with Audacity software. The latter was set at "0.031" input gain, at which preliminary tests showed +2.0 dBV into the interface recorded at -0.2 dBFS (dB referred to full scale); thus the maximum recorded signal level in the dynamic experiment approached -4.9 dBFS.

Figure 6: Spectrogram of Fender optical tremolo, comparing triode and resistor sources.

Figure 6. Spectrographic analysis of recorded Fender optical tremolo signals obtained by tremolo-loading either the relevant vacuum triode stage (left) or a 38-K-ohm resistive source impedance (right), which is an experimental control showing LDR distortion only. All plots are products of Spectrogram 16 software. The top panel shows the recorded waveform (across the top) aligned with the spectrogram. The four bottom panels show spectra at the time-points marked by the corresponding vertical green (near amplitude maxima) or red (at amplitude minima) downward-pointing arrows; in these panels, plotted peak amplitudes of the fundamental (1.0 KHz) and second harmonic (2.0 KHz) are compared. The amplitude color scale for the spectrogram is shown at upper right; note that it spans the 30-dB range ("-90" to "-60" dB) decorating the right side of only the second and fourth spectrum plots, but it applies to all four. About four seconds each, the original experimental sound-files are: TremRecTriodeSource.wav and TremRecControlSource.wav. The analysis shown here used a shorter edit built from four tremolo-cycles of each file in the order listed; it is TremEditTriode-Control.wav.

Four tremolo cycles of each recording (triode and control source) were pasted into a single brief WAVE file, which was analyzed using Spectrogram 16 software and the results presented in Figure 6. Notice that the time-domain representation (waveform envelope) above the spectrogram closely matches the modulation waveshape observed in the previous article using a DC test "signal" with the Fender LFO driving the AES replacement optocoupler (compare with Figure 11 [upper left panel, lower trace] in previous article, although different LFO frequencies were used). The spectrogram gain and color scale settings were adjusted to highlight the time-evolving detail in the second and third harmonics; this setting heavily saturated the fundamental (1.0 KHz). Harmonics above the third were not visible at these settings, so the spectrogram was configured to display about 3.5-KHz bandwidth for Figure 6.

Spectrogram 16 allows one to click on any time-point in the spectrogram window to display the "instantaneous" spectrum there, and the bottom four panels in Figure 6 show such spectra for the time-points at the green or red vertical arrows (at examples of amplitude maxima or minima, respectively). The absolute amplitude scales of these spectra show maximuim fundamental peak values ("-13 dB") which are lower than expected (-4.9 dBFS) based on the recording level. Presumably the difference is related to the software's gain structure or setting. In any case, it's the differences between peak values which are relevant. For the second harmonic, differences to the fundamental are indicated by brackets drawn in the spectra. With the tremolo-loaded triode, the second harmonic is 39.5 dB below the fundamental (1.0 percent distortion) when the audio signal is near maximum amplitude, and 35.5 dB below the fundamental (1.7 percent distortion) at amplitude minima. This is a relative increase in second harmonic distortion of 4 dB during the tremolo's attenuation phase, or 2.7 dB short of the 6.7-dB prediction from the static experiment (see discussion below Figure 5). I will demonstrate momentarily that most of this discrepancy could be due to photocell non-linearity. Note that tremolo attenuates the 1.0-KHz fundamental by a maximuim of 16.5 dB ("-29.5" versus "-13 dB"), confirming that this dynamic test can be compared directly with the earlier static test.

By substituting a 38-K-ohm resistive source impedance for the triode circuit, the control experiment (right-hand side of Figure 6) isolates harmonic distortion due to the photocell. In that case, detectable second harmonic distortion occurs only in the attenuation phase, while the neon lamp illuminates the LDR. This abruptly transitions to third harmonic distortion during recovery in darkness, and this distortion progressively decreases during recovery. With the triode source, the third harmonic occurred with the same dynamics and nearly the same amplitude as in the control, suggesting that most of it was caused by the LDR. In contrast, the triode source caused much more second harmonic distortion than the LDR; at maximum attenuation, the difference was 15 dB (-35.5 dB for the triode versus -50.5 dB for the control). Depending on its phase, second harmonic distortion due to the LDR could either reinforce or diminish distortion due to the triode, by a maximum of about 1.5 dB in this experiment. As I demonstrate next, the arbitrary LDR polarity that I chose caused the LDR to interfere with (subtract from) the triode's own second harmonic distortion. Thus, at maximum attenuation, if the LDR behaved like a linear resistor, second harmonic distortion with the triode source may have been -34 dB below the fundamental  instead of -35.5 dB, accounting for more than half (i.e., 1.5 dB) of the 2.7-dB discrepancy between static and dynamic triode results noted above.

Digging Deeper into Distortion Due to the Photocell. To better understand distortion due to the AES replacement optical isolator's LDR, I tested the device under steady-state (static) conditions as shown in Figure 7. The audio signal path used a 38-K-ohm resistive source impedance, as in the dynamic experimental control. The output shunt impedance was also the same as in the dynamic test, but measurements used the distortion analyzer and oscilloscope rather than spectrographic analysis of a recorded signal. The neon lamp was operated at various constant currents, hence constant light outputs, as done while characterizing opto-isolators in the previous article (see Figure 8 in previous article, specifically the green curve for the AES device).

Figure 7: Static experiment characterizing distortion due to LDR in replacement opto-isolator for Fender tremolo

Figure 7. Static analysis of audio distortion due to the LDR of the replacement Fender tremolo opto-isolator obtained from AES. The schematic diagram at upper right shows the test circuit. The graph at upper left shows signal attenuation versus neon lamp current. Aligned below that are distortion measurements for three different constant EIN levels: those which made EOUT 3.0, 2.0, or 1.0 VRMS when the lamp was off (red, green, and blue curves, respectively). At right, the top two oscilloscope images correspond to the indicated data points in the distortion graph, and the image directly below each shows the effect of reversing the polarity of the opto-coupler's LDR leads.

With its black curve and data points, the graph at the upper left of Figure 7 shows the optical isolator's signal attenuation characteristic versus neon lamp current, in a network whose impedances match that of the Fender tremolo circuit. This result is consistent with the steady-state LDR resistance measurements reported in the earlier article. The maximum attenuation (peak lamp current) obtained in the dynamic test (Figure 6) is indicated. Below that graph are total harmonic distortion readings at three different amplitudes; the red data points and curve (for 3 VRMS output at minimum attenuation) used the same input amplitude as in the dynamic test. At any given lamp current, distortion decreased with decreasing signal amplitude. For most of the test range, with input amplitude held constant, distortion decreased with increasing lamp current (light intensity). The lower current range resulted in somewhat erratic measurements, however, which I depict using the dashed part of each distortion curve in Figure 7. Some of the issue may be related to deminished stability of light output at low current. But on a time-scale of minutes, I also noticed a significant effect of light history in this range: If the lamp had recently been operated at relatively high current, I measured more distortion than if the LDR had recovered in darkness for a while. It required about 30 minutes with the lamp off (0 current) to reach minimum distortion for that condition; this is the black datapoint equalling the test signal's 0.015-percent background distortion level.

The graph in Figure 7 indicates that maximum photocell distortion occured in the relatively low (but non-zero) lamp current range. Such conditions also favored the most-pure second harmonic residue, as seen in Figure 7's oscilloscope images. In relation to the signal at EOUT, the phase (and apparently also amplitude) of the distortion product depends on which LDR polarity is selected. By chance, the dynamic experiment used (arbitrarily designated) "normal" polarity, as in the top row of 'scope photos. Second harmonic distortion caused by the triode (see Figure 5) is 180 degrees out of phase with that caused by the LDR in "normal" polarity. Therefore, while the distortion contribution of the LDR is small compared to the triode's, depending on how it is hooked up, it can either subtract from or add to tremolo-loaded triode distortion. The dynamic experiment in Figure 6 happened to use subtraction polarity.

In power terms, apparently the contribution of the photocell to overall Fender optical tremolo non-linearity is at least an order of magnitude (10 dB) smaller than that of the triode driving it. So I hesitate to belabor the subject. However, before concluding, I should say that different photocell types are likely to give different results. A recent internet search on audio distortion by photocells yielded little specific data. The Wikipedia page on resistive opto-isolators briefly discusses non-linearity, referring mainly to Perkin-Elmer's 75-page photocell and Vactrol datasheet, which states on page 35:

"Analog Optical Isolators have found wide use as control elements in audio circuits because they possess two characteristics which no other active semiconductor device has: resistance output and low harmonic distortion. AOIs often exhibit distortion levels below -80 dB when the voltage applied to the photocell output is kept below 0.5V.

"Figure 3 shows the typical distortion generated in typical AOIs. The distortion depends on the operating resistance level as well as the applied voltage. The minimum distortion or threshold distortion shown in Figure 3 is a second harmonic of the fundamental frequency. The actual source of this distortion is unknown, but may be due to some type of crossover nonlinearity at the original (sic; origin?) of the I-V curve of the photocell."

It goes on to say that odd-order harmonics (especially the third) dominate "at high AC voltages," where DC offset adds even-order harmonics as well. For four different Vactrols (VTL5C1 through VTL5C4), their "Figure 3" shows total harmonic distortion increasing as applied voltage increases at both 3-K and 30-K cell resistance, distortion being uniformaly greater at the higher resistance. This general characteristic agrees with my static results for the AES optical coupler (Figure 7). But there is no mention of a distortion burst at the onset of dark recovery, as observed in dynamic tests with the AES unit (Figure 6). Since I had an intact VTL5C1 on hand (and also having studied one such device's excised LDR in the previous article), I made a quick recording to survey distiortion in that Vactrol, shown in Figure 8 compared to an alternative dynamic test on the AES replacement opto.

Figure 8: Spectrograms showing distortion due to LDR in VTL5C1 (left) and AES replacement opto-isolator (right).

Figure 8. Spectrograms showing audio distortion due to LDR in VTL5C1 Vactrol (left) and AES replacement opto-isolator (right). These are screen-captured outputs of Spectrogram 16 software. The 1.0-KHz input was supplied via a 38-K series resistor and the LDR was shunted by a 37.7-K resistor in series with Behringer UCA222 input (as in Figure 3); amplitude across each dark-state LDR was 3.0 VRMS, for AC conditions exactly like those on the right-hand side of Figure 6. Spectrogram color scale (at right) and gain were also like Figure 6, but a longer time-scale and greater bandwidth is used in this Figure. With the VTL5C1's LED hooked to a regulated DC power supply via a 1-K series resistor, light intensity was manually increased in steps using the supply's voltage knob; the return to dark-state (at about "11 sec") also used the knob and thus was more a quick fade than an instant switch-off. In contrast, the neon lamp of the AES opto-coupler was SCR-gated with a symmetrical square waveform (approximately 0.4 Hz) as described in Figure 4 of the previous article, switching the lamp instantly between zero and 0.84 mA. The complete audio files represented here are: TremRecVTL5C1-step-mod.wav (about 11 sec) and TremRecAES-sqr-wv-mod.wav (about 7 sec).

Modulation methods for the two opto-isolators compared in Figure 8 differed: Current in the VTL5C1's LED was manually stepped through different levels using a DC power supply's output knob. The lamp in the AES unit was switched on and off with a 0.4-Hz square wave. But the audio amplitude and recording conditions were identical (the same as used in Figure 6). And a common feature of the two recordings in Figure 8 is that each coupler's LDR was held for about one second at a similar low-resistance (illuminated) state before a quick return to darkness. As shown earlier, the main distortion product of the AES unit with its lamp on was the second harmonic, and it held a constant level during constant illumination. In contrast, the Vactrol generated a series of odd harmonics while its LED was active; the third harmonic was predominant, and the higher-order harmonics progressively became detectable with greater LDR resistance (and less signal attenuation), as one looks toward the left side of the spectrogram. During recovery from illumination, each different LDR transiently produced odd harmonics dominated by the third (for the AES unit, at least the fifth is detectable with increased spectrograph gain). These were much more prominent with the VTL5C1 than the AES optical coupler, but the timing of their decay appeared similar.

What is the Significance of Non-Linearity for Fender Optical Tremolo Tone? In general, two aspects of tube amplification non-linearity are responsible for "good tone." One is a gradual onset of peak limiting ("soft clipping"), which sounds much more natural than the abrupt threshold-limiting characteristic of most solid-state amplifiers. The other is even-order harmonic distortion (mainly second harmonic) due to Class-A vacuum triode preamplification; at exactly one octave above the fundamental, the second harmonic is always consonant, generally heard as adding "warmth" or "fatness." This is the aspect most relevant to optical tremolo tone.

Relative to the fundamental, the proportion of second-harmonic distortion generated by any vacuum triode Class-A amplification stage increases with input amplitude. For the optical tremolo-loaded triode in Fender amps, this distortion also increases during tremolo attenuation phases. Thus, while optical tremolo modulates both the fudamental and the harmonic distortion product, modulation is always deeper for the fundamental. Judging from Figure 5, this depth difference may be insignificant at small input amplitudes. If there is an effect of distortion modulation on perceived "warmth" or "fatness" of the tremolo, it is probably greatest in the higher volume range. The dynamic experiment in Figure 6 placed 3 VRMS (about 8.5 VP-P) across the photocell during minimum attenuation phases, representing approximate conditions expected at high volume settings--probably near full rated power. (I have not measured or modeled typical input sensitivity at the power amp's polarity splitter, which would be the critical parameter for an exact statement.)

Of course, speculations about optical tremolo's affect on tone is complicated by multiple interacting sources of non-linearity when the whole guitar amp is considered. The power amp stages (polarity splitter and push-pull pentode output stage) has a differential architecture within a negative feedback loop. It should not normally generate very much second-harmonic distortion; instead it contributes mostly odd-order harmonics while peak limiting. The preamp stages are responsible for most of the amp's second harmonic. Since each preamp stage inverts the signal, to a first approximation, "Vibrato" channels with two stages (models without reverb) should tend to cancel out second-harmonic distortion compared to those with three stages (reverb-equipped amps). Of course, factors such as phase-shifts in the tone control network and uneven distribution of gain between the stages conspire to complicate the effect of even/odd triode number.

It may be difficult to argue that the low relative distortion contribution of the optical coupler's photocell (and its arbitrary polarity) could audibly affect the tremolo. On the other hand, the "voice" of any musical instrument, including celebrated vintage tube amplifiers, depends on the interaction of many non-linear functions; few would argue that subtlety does not regularly sit in with the ensemble. This is the challenge of those seeking to understand, repair, emulate, or digitally model a classic musical instrument: Does your concoction account for sufficient subtlety to make it respond like the real thing?

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