Rectification & Snubbers

No article on power supply design would be complete without addressing the subject of rectification and snubbers. These areas have received renewed interest within the DIY audio community, and appear surrounded by much folklore and mystique. My goal with this page is to provide the underlying scientific background; or the grain of truth from which the folklore and mystique took root. In addition, I will provide two snubber design procedures, and examine the impact of snubbers on a real-world amplifier.

No data exist to indicate that the inclusion of snubbers has any impact whatsoever on the DC output voltage of a power supply, or that they have any impact on the measured or perceived performance of an audio power amplifier connected to the power supply. However, snubbers may be warranted or required in order for audio equipment to pass regulatory requirements regarding electromagnetic emission, such as those imposed by the FCC in the US or the EU. While meeting such requirements is technically not required for DIY circuits, I certainly support that DIY equipment should be constructed with these requirements in mind. Do note, however, that any included snubber should be designed properly, as a poorly designed snubber may actually make the electromagnetic emissions worse.

Outline

Rectification

The schematic for a typical audio amplifier power supply is shown below.

The mains voltage enters the power transformer where it is transformed to the secondary voltage. This voltage is then rectified by the bridge rectifier, smoothed by the reservoir capacitors, and presented to the load. Power supplies as simple as this one, have been used for decades in both DIY and professional gear, and work quite well. They are not perfect, however.

The Non-Idealities of Rectification

The imperfections arise from the transformer non-idealities (i.e. parasitic components) and the turn-off characteristics of the rectifier diodes. The transformer parasitics are distributed throughout the transformer, and can be modelled by the lumped component circuit shown below.

The transformer parasitics consist of the magnetizing inductance (LM), the inter-winding capacitance (C), leakage inductance (LS), and winding series resistance (RS). If desired, these parasitics can easily be measured using an impedance analyzer or LCR meter as follows:

  1. Short-circuit the primary of the transformer.
  2. Measure the impedance of the secondary and determine its series inductance and series resistance. These will reflect the leakage inductance (LS) and winding series resistance (RS), respectively.
  3. Disconnect the short circuit from the primary of the transformer and leave the primary open-circuit.
  4. Measure the impedance of the secondary.
  5. The measured capacitance is the inter-winding capacitance (C), and the measured inductance is the sum of the magnetizing inductance (LM) and the leakage inductance (LS). However, as the magnetizing inductance is orders of magnitude greater than the leakage inductance, the measurement mostly reflects the magnetizing inductance.

During normal operation of the power supply, the transformer primary is connected to the mains, hence, the primary is loaded by the very low impedance of the power grid. This impedance is reflected to the secondary side by the transformer in parallel with the magnetizing inductance and the inter-winding capacitance, thereby effectively shorting out these two components. Thus, the remaining transformer parasitics (LS and RS), the PCB layout capacitance, and the rectifier diode capacitance form a parallel resonant circuit with the loss element (the resistor) in series with the inductor as shown below.

The presence of this resonant circuit is not problematic in itself. When the diode bridge is conducting, any energy stored in this resonant circuit is dissipated in the load. However, when the rectifier diodes stop conducting, the energy stored in the secondary resonant circuit will result in a little ringing, until it is dissipated in Rs. The frequency of the ringing tends to fall within the AM radio band, hence, it may be problematic from an electromagnetic compatibility perspective.

Reverse Recovery Characteristics of the Rectifier Diodes

One approach to minimizing the electromagnetic emissions is to select the rectifier diodes such that they provide as little excitation of the parasitic resonant circuit as possible. This can be accomplished by selecting diodes with desirable reverse recovery characteristics.

The reverse recovery of a generic PN junction diode is illustrated below (adapted from Blencowe, 2010, Fig. 2.12).As the voltage across the diode (blue curve) approaches zero, the current through the diode (red curve) approaches zero as well. However, it takes a finite amount of time for the charge within the diode junction to exit the junction. Thus, the diode will continue to conduct for a short time (the reverse recovery time: TRR), even as the reverse bias increases across the diode junction. The amount of charge that flows through the diode during the reverse recovery (QRR) can be determined by integrating the diode current during the reverse recovery time. These parameters are generally available in the diode data sheets.

Many savvy DIYers have taken note of the reverse recovery and have selected ultra-fast (low TRR) diodes or Schottky diodes (TRR = 0) for rectification. However, such diodes tend to cause very abrupt changes in the diode current as they turn off, which maximizes the excitation of the parasitic resonant circuit in the transformer secondary. Recall that the voltage across an inductor is:

    \[ V_L = L \frac{\partial i_L}{\partial t} \]

Where ∂iL/∂t is the rate of change in the inductor current. Abrupt changes have the highest ∂i/∂t, thereby, providing higher levels of excitation of the resonant circuit. Thus, I propose that rectifier diodes are selected for a low QRR and a soft recovery (low ∂i/∂t during reverse recovery), rather than simply selecting the diodes for a low reverse recovery time. Faster diodes (lower TRR) will possibly result in lower switching losses, but any switching loss caused by the reverse recovery charge is likely to be orders of magnitude below the losses associated with diode forward conduction. As such, these switching losses can safely be ignored.

Thankfully, the various semiconductor manufacturers offer plenty of diodes optimized for rectification of mains frequency voltages. They are usually marked as such on their respective data sheets.

Snubbers

In some cases, even careful selection of the rectifier diodes may not provide sufficient reduction in RF emissions to meet emission standards. In such cases, a snubber is needed. The main purpose of the snubber is to either reduce the frequency of the ringing that occurs when the rectifier diodes turn off, or to dissipate the energy stored in the transformer parasitics, thereby reducing the ringing. The frequency of the ringing can be reduced by adding capacitance in parallel with the transformer secondary, as illustrated by Cx in the figure below. This dramatically reduces the electromagnetic emissions, as the frequency of the ringing is lowered to the point where it cannot couple effectively into other circuits. Cx = 100 nF is commonly recommended and appears to offer sufficient EMI suppression to meet regulatory requirements.

Some prefer to take this a step further by using a snubber designed to dissipate the energy stored in the secondary resonant circuit. Technically, all that is needed for this is a resistor, but simply attaching a resistor across the transformer secondary would result in large amounts of power dissipated in the resistor. Thus, a capacitor (Csnub) is inserted in series with the snubber resistor (Rsnub).

To find optimal values for Csnub and Rsnub some authors will attempt to derive a mathematical model of the system. While this is an honourable goal, these authors make a series of approximations in order to find an analytical solution to the equation system. Unfortunately, these assumptions are often not justified in practical cases; including in the case of Johnson (2015). Thus, I find an experimental approach to be more informative and applicable in practice.

Simple Snubber Design

The component values of the snubber are actually not very critical. In practice an RC snubber consisting of Rsnub = 10 Ω and Csnub = 100 nF (Cx is left open) provides complete elimination of the resonant ringing from the transformer parasitics with a wide array of transformers (Elliott, 2019). There is nothing gained by adding Cx. In fact, it will only increase the amount of power dissipated in Rsnub.

Optimal Snubber Design

Some may wish to further optimize the snubber, for example by minimizing the amount of power dissipated in the snubber. This is accomplished by optimizing Csnub.

The purpose of Csnub is to ensure, that the energy stored in the parasitic components when the rectifier turns off is dissipated in Rsnub. For Csnub to accomplish this, its admittance must be significantly higher than the admittance of the parasitic capacitance in the circuit. Thus, to determine the optimum value for Csnub, the parasitics must be known.

Most circuit designers lack the electromagnetic field solvers required to determine the PCB parasitics and the LCR meter or impedance analyzer needed to determine the transformer parasitics. In addition, the parasitics of the rectifier diodes are highly nonlinear and voltage dependent, in particular at the transition from forward bias to reverse bias. Thus, the most reliable approach is to determine the parasitics experimentally at the desired working voltage of the circuit. This can be accomplished using an oscilloscope and a simple RC highpass filter as shown below (adapted from Elliott, 2019).

Do note that the output of the power supply must be floating (i.e. not connected to any ground). Otherwise, the power supply is short circuited through the oscilloscope ground connection. To prevent any large electromagnetic fields from coupling into the oscilloscope probe ground lead, I recommend minimizing the loop area of the probe ground connection by twirling the ground lead around the probe body or by using a grounding spring clip.

The image below shows the results of such a measurement performed on a Power-86 powered by an RS Components P/N: 177-945 power transformer. Note the large flyback spike caused by the inductance in the secondary circuit followed by the slight ‘buzz’ as the energy in the resonant tank is dissipated in the loss elements in the circuit. Also note that some transformers have enough loss to prevent the ‘buzz’ altogether. In such cases, no snubber is needed.

The optimal snubber is designed as follows:

  1. Measure the frequency of the ringing using the oscilloscope. As noted in the figure above, the frequency of the ringing in this case measured 877 kHz.
  2. Gradually increase the capacitance across the secondary by connecting progressively larger capacitances for Cx. Increase Cx until the ringing frequency has been reduced by half as shown in the measurement below.
  3. The parasitic capacitance of the secondary circuit can now be determined as: CPAR = Cx/3. In the measurement above, Cx =  5.6 nF was required to halve the frequency of the ringing, thus, CPAR = 5.6/3 = 1.88 nF.
  4. Remove Cx from the circuit.
  5. To ensure that the majority of parasitic circuit current flows through Csnub, select Csnub as follows: Csnub = 10·CPAR. Select the nearest higher standard value for Csnub. Thus, for the example above, Csnub should be: 10·1.88 nF = 18.8 nF. I chose the nearest higher standard value of Csnub = 22 nF.

Rsnub is generally optimized to provide a resonant Q in the range of 0.5 (critically damped) to 0.7 (highest Q that does not result in ringing). The quality factor, Q, for a parallel resonant circuit can be calculated as:

    \[ Q = \frac{R}{X_C} \]

where XC is the reactance of the capacitance in the resonant circuit and R is the parallel resistance. Thus, the resistance required to yield the desired resonant Q can be calculated as:

    \[ R = Q \cdot X_C \Leftrightarrow R = Q \: \frac{1}{2 \pi \cdot f_0 \cdot C} \]

I suggest designing for Q = 0.7 and choosing the nearest lower standard value for Rsnub. This provides the fastest dissipation of the energy in the parasitic circuit and completely eliminates the ringing, thereby completely eliminating any possibility of RF emissions associated with the ringing. The values for f0 (the frequency of the ringing without snubber) and the parasitic C (CPAR) were identified in steps 1 and 3, respectively.

  1. Thus, Rsnub is calculated as:

        \[ R_{snub} = \frac{0.7}{2 \pi \cdot \left ( 877 \cdot 10^3 \right ) \cdot \left ( 1.88 \cdot 10^{-9}\right )} \Rightarrow R_{snub} = 67.5 \: \Omega \]

  2. Choose the nearest lower standard value: Rsnub = 56 Ω. The resulting transient response is shown below.

For comparison, I repeated the measurements with the snubber replaced by the snubber obtained from the simple snubber design procedure (Rsnub = 10 Ω, Csnub = 100 nF). The result is shown below. As seen below, the simple snubber also results in a response that is free of ringing.

To maximize the efficacy of the snubber, the parasitic inductance of the snubber itself should be minimized. Thus, wire lengths and PCB trace lengths in series with the snubber should be minimized.

Observant readers will note that I use IEC E12 standard values. These component values are commonly stocked by the various component distributors. If you would rather use values from the E24 series (±5% tolerance) or E96 series (±1% tolerance), you are free to do so. Note, however, that the exact values of the snubber components are not all that critical.

Impact of Snubbers in Audio Amplifiers

Many DIYers are likely more concerned with any audible impact of the snubber than they are about eliminating RF emissions from the rectification. To address this concern, I designed an experiment to measure any impact of the snubber on the output of an audio amplifier.

In order for the snubber to have any impact on the circuit connected to a power supply, it must cause a change in the output voltage of the supply. As the DC voltage on the output does not change with the addition of a snubber, such a change must be in the ripple or noise superimposed on the DC output voltage. Thus, I measured the ripple and noise voltage at the output of a Power-86 Rev. 1.2 powered by an RS Electronics P/N 177-945 (2 x 35 V) power transformer. The supply was loaded with an 8 Ω load on each supply rail and the presence of rectifier ‘buzz’ without snubber was verified. The result is shown below for two different snubber types: No snubber and optimized RC snubber.

As expected, the snubbers made no difference in the output ripple and noise of the power supply. Thus, it is rather irrational to expect it to change the output of the amplifier through the power supply.

Alternatively, it is possible for the RF energy emitted by the transformer parasitics to couple inductively into the amplifier, thereby degrading the amplifier output. To test this hypothesis, I used an LM3886DR Rev. 1.0 powered by a Power-86 Rev. 1.2. The power transformer was an RS Electronics P/N 177-945 fed from a variac, which allowed the supply voltage to be adjusted to ±30 V. At the beginning of the experiment, it was verified that diode ‘buzz’ was present at the transformer secondary with no snubber connected.

I chose the LM3886DR as it is very representative of a typical DIY audio project. Furthermore, the power supply rejection ratio (PSRR) LM3886 is somewhat low, which makes this amplifier more sensitive to perturbations of the power supply voltage. Thus, the LM3886 should have the greatest chance of any of my amplifiers to show any benefits of using a snubber.

I measured the amplifier output at idle and near clipping with a 4 Ω load for the two snubber types: No snubber and optimized RC snubber. This operating point was chosen as it provides the greatest amount of diode buzz, thus should show the greatest impact of using a snubber.

The results are shown below. For all intents and purposes, the measurements are line-on-line. I.e., there is no difference in the amplifier output when powered by a power supply without snubber and when powered by a power supply with a fully optimized snubber.

For completeness, I measured the multi-tone IMD for the two snubber types as well. This test signal is essentially a deterministic version of a music signal and is, thus, presents a realistic view of the amplifier’s performance with a music signal. The measurement is shown below. Again, the two test conditions measure identically.

Finally, I measured the THD+N vs output power at 1 kHz with an 8 Ω load for the two test conditions (no snubber and optimized RC snubber). This operating point was chosen as it offers the lowest THD+N of the LM3886, thus, has the greatest possibility of showing any ‘crud’ injected from the power supply. The measurement is shown below.

Not surprisingly, the measurements showed no impact in the amplifier output from the addition of snubbers.

Perspective

While “geeking out” over snubbers is mostly a harmless exercise, it is also largely an exercise in futility, in particular for those concerned with the presence of “nasty signals” within the amplifier enclosure. While snubbers do somewhat reduce the amplitude of the flyback spike that occurs when the rectifier diodes turn off, they do not eliminate it. Thus, its potential for inductive coupling into sensitive nodes remains.

A far nastier signal present within the amplifier enclosure is the charging current flowing through the rectifier diodes into the reservoir capacitors. Recall that the rectifier diodes only conduct when the secondary voltage of the transformer exceeds the voltage on the reservoir caps. Thus, the diodes only conduct for a small fraction of the mains cycle. As the charge drained by the load will need to be replenished while the diodes conduct, the charging current can be significant, and often reaches tens of ampere even in a modest power amp. Furthermore, the charging current is a pulse train, which further increases the potential for electromagnetic coupling.

The graph below shows the charging current of an LM3886DR amplifier delivering 1 kHz at 60 W into a 4 Ω load (measured using a Triad CST-1030 current transformer terminated in 100 Ω). Note that the vertical scale is 2 A/div.

Rather than adding components to your power supply design, I suggest following sensible chassis layout practices by routing sensitive signals (in particular the amplifier input connections) away from the rectifier and transformer wiring to the extent possible.

Conclusion

In some cases, snubbers may be required in order for equipment to pass regulatory requirements regarding electromagnetic emissions. While minimizing electromagnetic emissions in DIY equipment is an honourable goal, it is by no means required.

Those who wish to minimize or eliminate the electromagnetic emissions associated with rectification will find that a simple C-only snubber of Cx = 100 nF or, even better, an RC snubber consisting of Rsnub = 10 Ω, Csnub = 100 nF will work well. For further optimization, please see the Optimal Snubber Design procedure above.

It should be noted, however, that the addition of snubbers makes no difference in the output of the power supply or in the output of the connected audio amplifier. Thus, any claims of audiophile superiority resulting from the addition of snubbers should be viewed with skepticism. This is especially true in the cases where the proponents of snubbers also sell you the tools for their implementation. As always: Extraordinary claims should be backed up by extraordinary evidence.

Rather than adding snubbers, I suggest following the current best practices regarding chassis layout and wiring. Particularly, I suggest routing the input wiring for the amplifier as far away from the power transformer as practically possible.

Finally, it should be noted that the diode ‘buzz’, and thus the need (whether real or perceived) for snubbers, can be eliminated by selecting rectifier diodes which are designed for bridge rectification. Such diodes are commonly marked as “intended for bridge rectification” on their data sheets and tend to feature a low reverse recovery charge and a soft recovery characteristic. Fancy high-speed diodes are by no means necessary for good power supply performance.

References

Blencowe, M. (2010). Designing Power Supplies for Tube Amplifiers. Wem Publishing. ISBN: 978-0-9561545-1-4.

Elliott, R. (2019). Snubbers for PSUs. Downloaded from: http://sound.whsites.net/articles/psu-snubber.htm.

Johnson, M. (2015). Soft Recovery Diodes Lower Transformer Ringing by 10-20x. Linear Audio Vol. 10.

 

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