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First filter cap value selection
Hi Guys

If you browse through a lot of schematics for audio gear, you see certain common values for the main filter cap immediately after the rectifier. How much if this is by design? How much is just copied from similar equipment? How do you know what the "right" value is?

Let's use our ubiquitous 50W push-pull amp model with these specs:
output transformer: 4kaa
100pk requires 316Vpk at 316mApk
tube saturation voltage is 60V
minimum plate voltage at full load: 316Vpk + 60V = 376V, call it 380Vdc

The effective load is then 380V / 316mA = 1k2

Assuming the plate winding on the power transformer has the usual 20% regulation, unloaded Va is then about 1.25 x 380V = 475Vdc. This would be derived from 330Vac. At full load, the winding voltage has fallen by 20% to about 270Vac and its 380Vpk is the relevant value to use.

We always use full-wave rectification for ALL windings, so the ripple frequency is twice the mains frequency, making the ripple 100Hz or 120Hz depending on where we live.

The approximate ripple voltage from a rectifier can be calculated using the ripple frequency, the peak voltage from the rectifier, and the filter cap value. Say we use 100Hz ripple for 50Hz mains and a 100uF cap to begin with.

Vripple = (Vpk x Tau) / (C x R-load)
where Tau is the reciprocal of frequency >> 1 / 100Hz = 0.01s, or 10ms,

Vripple = (380Vpk x 10ms) / (100uF x 1k2)
          = 31V7ac

Truly, this is going to be marginal with respect to not having the output signal being modulated by AC ripple.

If we double the filter cap value the ripple will be half - 16Vac - a straight linear relationship BUT with diminishing returns if we go too large. 1mf (1,000uF) would cut the load ripple to just over 3V and this is what hifi guys do in their tube amps, often followed by a massive choke into another 1mF cap Big Grin Great if you do not want to add solid-state hum filters.

In the past, high-voltage capacitors of this value range were not available and series-parallel banks would be needed. The cost would be prohibitive and the bulk of components needed to be managed. Now that snap-mount caps are affordable and of tremendous quality, there is no excuse for under-filtered power supplies EXCEPT for equipment that is never expected to be driven to its maximum capability. A music amp used to be such a device, although nowadays there is so much compression used in recording that peak-versus-average levels have narrowed. In a guitar amp, under-filtering is historic and thus copied widely. This means that any amp driven to clipping is also likely to exhibit a lot of hum - witness Komet amps, Tranwrecks, some plexis, and all their clones.

A very reasonable observation is to use a PT with better regulation, or at the very least use one rated for a bit higher voltage so that the sagged voltage will not modulate the output even at clipping. In TUT5's Stentorian chapter, you may recall that polypropylene caps were used as supply filter. The caps were 47uF each and that with three caps the clipped signal output was hum-modulated but at four caps it was clean - 141uF changed to 188uF. This result would have been the same were the caps electrolytic.

When you go to lower voltages as found in solid-state amps, the cap values are necessarily much higher.

Say we have a 100W amp at 8-ohms, which requires a peak signal of 40V at 5A. The saturation voltage of BJTs and mosfets is quite low and we may only need a few volts. Let's say, this is 5V. We now have an effective load of 45V / 5A = 9-ohms. We will use the same 50Hz mains >> 100Hz ripple >> Tau = 10ms.

We are being thrifty and try 1,000uF first (1mF):
Vripple = (45V x 10ms) / (1mF x 9)
           =  450mV / 0.009
           = 50Vac ???

This is more ripple than AC voltage coming in to the rectifier, so this value must be ridiculous or we have a wonky equation? If we go to a more common value of 10mF, at least the ripple is more reasonable at 5Vac.

Since the solid-state amplifier is likely to use symmetric supplies, it is a common assumption that half the power comes from either side of the PT center-tap - indeed it does over the complete signal cycle, but each peak is carried fully by just one side at a time. The "averaging" assumption would have the effect of making the load seen by each side twice as high in value and potentially reduces the ripple voltage to 2V5. This assumption is often used in assessing the ripple current rating required for the filter caps.

In both the tube and solid-state examples, it is clear that it is highly beneficial to have an idle DC voltage quite a bit higher than the expected loaded value, not just to accommodate supply and mains regulation, but to accommodate insufficient ripple reduction.

In any case, the first filter capacitor is the main element in fighting ripple through the supply line, so skimping on its value is never a good idea.
Thanks for all the info! I Agree with you that low ripple requires more capacitance in first filter cap. As we know (and often mentioned in the TUT series) some of the feel of some of the older amps comes from the poor power supply regulation and sag that creates. I usually up the amount capacitance in amps I build that are based on old designs but then find I need to add sag resistors or SUS to try get more of a vintage feel. What circuit approaches do you favor for players who want a vintage feel but want to have nice quiet power supply?
Hi Guys

Yes, having larger main and subsequent filters will stiffen the supply apart from improving noise performance. I always take the performance improvement over preserving natural sag. In most cases, because I choose to use over-sized PTs to have lower transformer temperature rise, this improves the supply regulation and reduces EMI from the PT. I end up with a pretty stiff supply. To enhance hum reduction, I always have active hum filters. All of this goes against the economically-driven PSU design of traditional guitar amps.

How do you soften things up? Get some sag effect? But without altering the super-low-noise supply?

As TUTs illustrate, adding low-cost resistors here and there will give you all the sag you desire. Or, add electronic circuits to provide user-controlled sag. All of this is post-nirvana-providing-raw supply so there is no noise penalty with whatever we do.

Note that added resistors in series with supply feeds, say to the output transformer, will introduce a signal-dependent voltage drop that has fast collapse and recovery times - as fast as the signal. There are no caps to recharge, and thus, it will sound different compared to whole-supply sag. If you add a cap to ground after the R, you have an RC constant for the recovery BUT this will only sound proper for a given signal current range. This is what one of Randall Smith's patents was for, which was worthless on two counts: the effect is limited to playing the amp near full output; patents do not cover circuit values... yet the USPTO took his money anyway.

The solution is to have a means to proportion the sag effect to the power level you wish to use, the loudness, regardless of whether the amp is Power Scaled or not. For this, London Power offers the SUS Sustain kits. These are NOT like a BOSS Compressor-Sustain pedal. Instead, SUS only changes the attack of the note, which can sound like the supply sagging or at least running out of headroom to pass the transient part of the waveform. This is a compressor side-chain approach. SUS can control the output stage or be installed further back at the splitter, or a preamp stage. You have to use the correct kit for whatever circuit block you are tying it to.

Alternatively, you could have switched resistors to provide the range of effect for different current levels corresponding to different loudness levels. This would be entirely passive and understood by tinkerers of most skill levels.

An alternate to the SUS approach or the passive one is to use an RMX technique from TUT4, again active, and also continuously variable.

If you are tailoring an amp to your own playing situation, many of the decisions become simpler. You can decide on a power output that is around what you need, then add passive elements to fine tune it. this is okay for playing the same place every time BUT maybe sometimes you play much bigger places?

One approach is to simply mic your small rig through a larger one for the extra coverage. Another approach is to have a larger amp tuned like the small one. A further approach is to have oine amp that can be used both places at the two different power outputs required, which can be achieved in countless ways.
Thanks for all the great info and was very helpful.

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