What is power supply sag and what to do about it? 
  30 Jan 2019  (updated 30 Dec 2023)
  Mike at MDBVentures.com
  http://www.MDBVentures.com - Great prices on great tubes!


Power supply sag is when the voltage supplied to the electrical circuits 
changes. Usually defined as voltage going down a bit or sagging. 
This is caused by the electrical circuit demanding more power than the
power supply can fully provide.  

In reality, all power supplies sag to some extent. In most cases it 
is so insignificant that it is not noticable. In cases where the supply 
voltage stability is critical, great care is used to minimize the sag
by using voltage regulators.

One area where voltage sag is often discussed is in tube based 
amplifiers. This is because often the circuits are minimal and thus 
are susceptable to sag. 

In a guitar amplifier sag usually happens when a string is initially 
plucked. This is when the biggest demand is placed on the circuits as 
the volume is normally the loudest at that point after which it fades 
as the string slowly reduces its vibration intensity. 

I've seen some references to the sag being caused by the rectifier 
tube not being able to supply the power and then "recovering". 
That is not quit what happens. The tube never "recovers", rather it 
is the entire power supply circuit that recovers. More specifically
it is the charge voltage on the filter capacitor that "recovers". 
Generally, the tube is the only part that is easily replaceable, 
so it usually gets the blame. 

Let's say the amplifier power supply can provide a continuous 100 milliamps 
at 100 Volts which relates to the amplifier generating a basic continuous 
sinewave at an amplitude of 1 Volt. With the volume control set to 
maximum and a string is plucked, the sinewave amplitude jumps to 
2 Volts. This puts a demand on the power supply of 200 milliamps. 
This is beyond what the rectifier can keep the filter capacitor 
charged at, so something has to give. What happens is that the
voltage across the filter capacitor will fall due to the excess demand 
on it. In the meantime at 120 times a second (assuming a fullwave 
rectifier circuit - 100 Hz for the 50Hz power folks), the rectifier 
tube will try to recharge the capacitor. The more current demand from 
the power supply, the more voltage drop across the rectifier tube. 
As a result, it will not be able to charge the capacitor to the same 
level it was at with the lower electric current demand. That means the 
voltage across the capacitor will be less (not to mention that it 
will be pulsating at 120Hz (or 100Hz) as each charge cycle comes 
around on the AC source). 

As the string vibration amplitude fades, the current demand on the
power supply is reduced and thus the current flow demand from
the rectifier tube to keep the filter capacitor charged is 
reduced, so the voltage drop across the rectifier is reduced, which
means that the voltage across the filter capacitor and thus the 
power supply voltage increases. The rectifier tube hasn't really 
"recovered", it is just acting normally. 
If the tube is weak, the resistance across the tube will be higher,
and that means the voltage drop will be higher, both at the normal
volume level and at the higher current demand, but it will likely
be more noticable at the louder volume level. 

So, what to do about sag? First keep in mind that sag is a component
in what makes the distinctive distortion sound of an amplifier 
when operating at maximum volume level, along with the clipping 
of the tube circuits. So, you may not want to actually "fix" it.

The one replacable component in the tube based power supply is the 
rectifier tube, so it is pretty much the only thing you can change 
to affect the power supply sag (other than turning down the volume). 
Since a rectifier tube increases its internal resistance as it gets 
used up, a new rectifier can keep the power supply charged up to 
a higher voltage under maximum load, meaning less sag. 

The same holds for trying a different type of rectifier tube. 
It is the internal resistance of the tube (as noted by the voltage 
drop across the tube) that determines how much voltage it can 
keep the filter capacitor charged to. The lower the resistance, the 
higher the voltage that gets to the filter capacitor. 

Note: The listed voltage drop and the internal resistance of the
rectifier tube, while related, are not the same thing. The voltage
drop specification is determined at a specific current level through
the tube, which is dependant upon the tube design. Thus a tube with 
a lower voltage drop may actually have a higher resistance at the 
same measurement current than a tube designed for higher current levels. 
To determine the internal resistance, check the specifications of 
the tube. If you can't find the resistance information, you can determine 
it by looking for the voltage drop rating, which is normally given at 
a particular current level. Divide the voltage drop by the current 
given to get the internal resistance. 
Example: A 5U4GB has a voltage drop of 50V at 275mA 
Thus the internal resistance is 50/0.275=182 ohms.

Another note:
The plate resistance measurement (dynamic plate resistance) used for 
amplifier tubes is not the same as that used for rectifier tubes 
(static or DC resistance) which is used to measure the emission of the tube.
To measure a rectifier tube, a voltage is applied between the plate 
and cathode. The voltage drop across the tube is then measured.
That provides the information on the "static" current and resistance 
of the tube which is the emission measurement. In the tube manuals, this
is generally specified as a voltage drop between the plate and cathode
for a given current through the tube (usually the max current for the tube). 
What is important in an amplifier tube is the gain of the tube, that 
requires a different type of measurement of the plate resistance, the
dynamic plate resistance. That is done by measuring the tube resistance
at two different Grid voltages. The difference between the two measurements
is the dynamic resistance (Rp) of the tube and is a measurement to determine
the the gain of the tube (Gm), not the emission. 


Why Arcing is Bad

As well as causing damage to the tube itself, arcing can damage the 
circuits in which the tube is used. When a tube begins to arc, it starts 
to tear apart the tube, especially the cathode material. This can create
a non-rectified resistance path between the cathode and plate. 
This has similar effects as a short between the cathode and plate. 
Meaning bad things happen.

What that means is that the tube no longer blocks the reverse electrical 
path. While that in and of itself is no worse of a problem for the tube
(the damage caused by the arcing itself being the real damage to the tube), 
the rest of the circuits will not be happy to have reverse voltage being 
applied to them. In particular rectifier circuits pretty much always 
have a filter capacitor that is polarized. If a reverse voltage is applied 
to a polarized capacitor, it will damage the capacitor, often resulting 
in catastrophic failure (ie the capacitor blows up).  

If the arcing continues for any length of time, the parts of the tube 
that the arc is tearing apart can start to lay down a electrical path
(sometimes called a carbon track), between the cathode and plate 
(and/or grid for non-rectifier tubes). 
This will permanently damage the tube, although the damage to the cathode
will already have degraded the tube to likely being useless anyway. 
The more the cathode is damaged, the fewer electrons it can release, which 
is equivalent to the tube quickly being degraded to end of life condition. 


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Understanding Rectifier Tubes

A simple way to look at a rectifier tube to better understand how it works 
is to see it as an ideal rectifier (a one way valve with no voltage drop) 
in series with a resistor. The resistance is fairly stable within the 
bounds of the normal current levels through the tube. It is the resistance 
of the tube that defines the voltage drop of the tube. Just as more current
through a regular resistor increases the voltage across the resistor, an 
increase in current through a rectifier tube causes an associated increase
in voltage drop across the tube. So the voltage drop is dependant upon the 
current through the rectifier tube. 

Note: Gas rectifiers are an exception to this as the plasma generated by the
gas tube during operation causes the current flow to follow plasma rules 
rather than vacuum tube rules. Plasma based retifiers are generally negative
resistance devices. That means they reduce the internal resistance as the 
current through the tube increases. This is because as the current increases,
more plasma is generated which provides more paths for the electrons to 
follow. That translates to a lower resistance. The result is that a gas 
rectifier will tend to have a constant voltage across it, whereas a 
normal rectifier tube will have a constant resistance (meaning the 
voltage drop changes with the current flow through the tube). 

Of course as with all things about tubes, these are only generalized 
aspects about the operation. Tubes are non-linear, especially at the outer 
limits of their normal operating parameters. However within the bounds
of their normal operating parameters, they will tend to be consistent.

The construction of a tube defines the resistance of the tube and that 
determines to a large extent the maximum current through the tube. 
The type of material used in the cathode coating and the heater voltage
and current determines how many electrons the tube can release. 
That together with the distance between the cathode and plate, which
determine how far the electrons have to travel determines the tube
resistance (gas rectifiers being the exception - see note above).   
The distance between the cathode/heater and the plate determines the 
maximum voltage the tube can handle. 

Another important part of the rectifier circuit is the filter. 
The rectifier itself is actually a part of the filter that is used
to convert the AC voltage into a DC voltage.

AC is used because it makes distribution of the electricity simple and
efficent. But it also means that to be used in most electronics it needs 
to be converted to DC. 

The AC contains a full sinewave of positive and negative voltage. 
The purpose of the rectifer is to block the unwanted half of the AC power. 
Usually the positive component. In a full wave rectifier circuit, 
the other half of the AC cycle is inverted (via the transformer) 
so that it can also be used. This makes the power supply more 
efficient by using both halves of the AC signal. 
Halfwave rectifier circuits only use one half of the AC power source. 
It is less efficent, but the circuit is also cheaper and can be built
without a transformer (which is why cheap radios use half wave
rectifier circuits). 

Once the AC is converted through the tube into a pulsing halfwave 
signal, it needs to have a capacitor to help smooth the power 
into a stable DC voltage. 

A note about AC power voltage measurement.
AC power voltage is measured as RMS (Root Mean Square). 
What this means is that instances of the voltage are sampled over time 
(measuring an instant in time of the various voltage levels of the 
waveform) and each resulting measurement is then squared and the 
result added to all the other squared measurements. The total result 
is then divided by the number of measurements and the square root is
taken of the result. The answer is then an idealized result of the 
voltage as if it had been a DC voltage instead of an AC voltage. 
The classic way to measure it is to apply the voltage to a precision
resistor and measure the heat generated. That is then compared to 
the heat generated when an equivalent DC voltage is applied to the
resistor. Since that method is not very accurate, it is pretty much 
never actually used. Modern meters just use the RMS calculation method. 

The peak voltage in an AC power source is 1.44 times the RMS voltage
and conversely the RMS voltage of the peak voltage in a perfect 
sinewave is 0.707 times the peak measured voltage. 
This is important to note because the DC voltage derived from an AC
power source will be 1.44 times the AC RMS voltage. Assuming a perfect
conversion, no resistance in the power supply and there is little or 
no load on the supply. 

Since there is a pulsating DC voltage that comes out of a rectifier that
has stripped off the unwanted half of the sinewave voltage, a device is 
needed to temporarily store electrons to smooth out the voltage to 
something stable (ie a DC voltage). That is the purpose of the filter 
capacitor. (A choke is sometimes used as well - we will get into that 
a bit later.)

The voltage that comes out of the rectifier starts out at zero volts at
the beginning of the half portion of the sinewave. The voltage then 
rises to the peak voltage in a little over 4 milliseconds (60Hz power), 
then falls back to zero volts again in a little over 4 millseconds 
(5 milliseconds for the 50Hz folks). It then stays at zero volts for 
a little over 8 milliseconds (10 millseconds for 50Hz) while the other 
half of the sinewave is being blocked. For a full wave rectifier, the 
other half of the rectifier tube is doing the same thing to the 
inverted half of the AC during the off time of the first section). 

So what the circuit does is that during the time that the voltage is 
available from the rectifier tube it pumps electrons into the capacitor
(referred to as charging the capacitor) as well as providing the 
electrons to the rest of the circuit. Then when the voltage drops 
below the voltage present on the capacitor, the electrons for the 
circuit will come from the capacitor instead of from the tube. 

The greater the current flow demand from the capacitor, the faster
the voltage it supplies drops. A bigger capacitor can hold more electrons,
so the voltage won't drop as rapidly for the same amount of current demand. 
However, a bigger capacitor will take longer to charge. So an important 
part of the power supply is picking a capacitor that is big enough to 
not sag the voltage too much under load, while still being small enough to 
be able to have an adequate charge injected into it during the charging 
part of the cycle. All of this while the overall circuit is demanding a 
variable amount of current depending on the signal being amplified 
by the amplifier. So the size of the capacitor (in microfarads) is an
important design decision. It must be big enough to supply the needed 
current with a minimum drop of the voltage, but small enough to be able 
to be charged up in time. The resistance of the tube is an important part 
of that decision since that determines how quickly the capacitor can be 
charged during the charging part of the cycle. 

When there is a smaller current demand on the power supply, the voltage 
on the capacitor will be higher. But when the current demand increases 
such as when the guitar string is plucked, the voltage on the capacitor 
will not just drop, it will also have an increase in ripple on the voltage
as the charge/discharge voltage levels on the capacitor increase. 
That can have some interesting effects, especially in simple circuits as 
can be found in many tube based guitar amplifiers, because the 120Hz 
ripple from the power supply can get into the audio being generated and 
cause distortion. 

In the very early radios, it was a problem because they were not able
to make reasonable cost filter capacitors with a large storage capacity, 
plus they were much more resistive than more modern capacitors. 
To compensate for that, an inductor was used to help smooth out the 
charge/discharge demand on the capacitor. 
An inductor builds up a magnetic field during the charge cycle, and 
in the process impeads the electron flow through the inductor as it 
is building the magnetic field, thus causing the voltage across the 
inductor to increase as it is charging (building the magnetic field). 
As the voltage from the rectifier begins to drop on the trailing side
of the AC power sinewave, the magnetic field around the inductor begins
to collapse, and that feeds more electrons into the capacitor. The effect
being that the voltage across the inductor gets smaller, and thus the 
ripple voltage across the capacitor is reduced as the inductor helps to 
keep the capacitor charged even as the AC wave voltage is dropping. 
That allows the use of a smaller capactor (in microfards) without the 
ripple becoming excessive. In power supplies, the inductor is usually 
referred to as a choke. In the early radios, the choke did double duty as
being the speaker magnet. 

In some cases, a current demand could be high enough to cause unacceptable 
ripple, so another stage of inductor/capacitor might be placed in series 
with the first stage. That can reduce the ripple, but at a cost of increased
inefficency and greater cost (chokes are big and expensive). 
If low power supply ripple is important (such as in a high gain amplifier), 
but the current demand is minimal (a few milliamps or less), often a resistor 
is used instead of a choke. A resistor is not as efficient and the votlage 
loss will be significantly higher, but resistors are small and cheap. 

When the ripple on the power supply voltage is still too high, a voltage 
regulator will be used to reduce the ripple. 

Voltage regulators come in three basic types. The first were simple shunt
regulators that used a neon gas filled tube to regulate the voltage
they simply added a variable load to the power source to keep a stable 
current drain through the supply. They were not usable for high current demands. 
Advanced designs used amplifiers to amplify the effects of the shunt regulator 
for higher currentg demands. 

Modern solid state electronics have allowed additional methods of regulation. 
The first active solid state regulators used Linear regulation. That involved
a transistor in series with the DC power source. By monitoriong the output 
voltage and adjusting the resistance of the transistor, the voltage can be 
constantly adjusted to very significantly reduce the ripple. The cost is 
efficiency. Linear regulators are typically only 60% to 70% efficent.
The wasted power is burned off as heat by the transistor. 

The demand for greater efficiency as well as improvment in solid state devices
and capacotors has caused the third type of voltage regulator to become more popular, 
the switching regulator. Unlike the linear regulator, instead of throwing away the
unneeded voltage as heat, the switching regulator turns the transistor on for
a short duration (as short as 100 microseconds or even shorter) to charge up the 
capacitor. By using very short duration pulses, the ripple is much less, and since 
the transistor is off between the charge pusles, it is not burning away the excess 
voltage as heat. That means that a higher voltage can be used on the input to the
regulator so that a higher amount of ripple is allowable. The result is power 
supply efficiencies of 90% or higher. 

Switching supplies do come at a cost though. They generate high frequency noise
which can get into sensitive circuits. If that is a problem, a linear regulator is 
often used after the switching regulator to get rid of the noise. But since the
switching regulator is operating at a high frequency and has reduced the ripple 
significantly, the linear regulator doesn't have to work as hard and can be 
significantly reduced in cost and size as well as being more efficent (75% to 80%).

Even a voltage regulator cannot stop the ripple entirely, but it can usually reduce 
it to the point that it is no longer an overwhelming problem. 
A voltage regulator works by monitoring the output voltage. If it sees the voltage
drop, it lets through more power to bring the voltage back up to the desired level. 
While the modern regulators can detect very small changes and quickly adjust to the
change, it still must allow a small shift to occur in order to be able to see that 
the voltage has dropped and needs to be boosted. 

------------
Trivia: Airplanes use 400Hz power instead of 60Hz or 50Hz so that 
the power supplies can be made smaller and more efficient. 
This is because at 400Hz, the amount of time between cycles is
2.5 milliseconds. That means smaller capacitors can be used and
the recharge time is faster so there is less waste heat being dumped.
The downside is that 50/60Hz based equipment won't work on aircraft 
power systems. The equipment has to be specifically designed for 
use on an aircraft power system. 

So if 400Hz is better, why don't we use it everywhere? 
The short answer is; Because over long distances, 60Hz/50Hz is more efficent, 
and since we aren't trying to defy gravity with land based equipment, the 
bigger and heavier (but cheaper) equipment is not a problem.

So why 60Hz, where did that come from? 
Since there are 60 minutes in an hour, and 60 seconds in a minute, it seemed
only natural to Tesla to use 60 cycles in a second for the A/C power.  

Although Thomas Edison came up with the concept of electric power distribution
first using 90 Volt DC, Nikola Tesla is the inventor of the 120 Volt A/C power 
system we use today. There was a long running dispute between the two men over 
which method to use for power distribution. Although the battle was intensly
fought with many legal, economic and social issues involved, ultimately the 
A/C power distribution method won for a very simple reason, over long distances,
A/C power was vastly more efficent than DC power. 

The reason why is because the longer the distance traveled, the more resistance
there is in the power lines and that means loss of voltage, which can be very
significant over long distance. This can be compensated to some extent with 
heavier wire, but it quickly becomes uneconomical to use massive copper wire
over long distances. 

The voltage loss is caused by the resistance of the distribution wires.
The longer the wire, the greater the resistance. That resistance impeads
the current flow through the wires. The greater the power demand (heavier 
current load), the greater the voltage loss. To compensate for the voltage
loss, the voltage at the power source can be increased. Unfortunately, 
since most distributed power has a highly variable load demand, that means
the loss is highly variable, resulting in the end point voltage being 
just as variable. 

A way to deal with the variable loss is to minimize the current flow through
the distribution wires. That can be done by increasing the power source voltage 
to a very high level, then reducing it back to the desired amount at the endpoint.
Unfortunately at the time, it was not easy to do that with the D/C power. 
The method available for D/C was motor/generators, which were expensive and being 
a mechanical solution also had a high maintenance cost and a reduction in reliablity
due to requiring the system be shut down periodically for maintenance. 
While the source generation for both methods required mechanical generators, beyond
that, the A/C power method allowed for a simpler and more reliable non-mechanical 
transformer to raise the voltage at the source (or simply generate it at the
higher voltage), and another transformer at the end point to reduce the voltage
to the desired working level.    

At the end-point usage, there was an additional savings for A/C power. 
The main usage for power distribution was electric lights and motors. 
While the electric lights didn't care if the power was A/C or D/C, the motors
had to be designed specifically for the type of power used. The problem with
the D/C motors was that they required the use of brushes to make physical 
contact with the motor's rotor. That ment a high amount of maintanace as the
brushes had to be periodically replaced. That was the other aspect of the
genius of Tesla's A/C power. For most of the uses, the A/C motors did not need 
to have brushes. No physical power contact with the rotor was required, which
drastically reduced the maintance cost. With good bearings, such motors can
last decades with no maintance at all.  

There is an irony to all this however. For very long distance power distribution,
D/C is actually more efficent than A/C when the problems and expense of up converting
and down converting the distribution voltage are removed from the equation. 
Which is why very long distance power distribution has been switching to using 
D/C on the distrbution power lines.

The A/C interacts with the enviornment (including the Earth's magnetic field),
this impeads the flow of the power through the lines to some extent. The magnetic
field of force generated by the power flowing through the lines can also interfer 
with nearby equipment. While D/C also generates a magnetic field, it is a fixed 
field (not cyclical), which while still interacting with the enviornment to some
extent, it is vastly less so, which reduces the losses caused by that interference.

With the advent of very high voltage solid state devices, voltage conversion for 
D/C power no longer requires the use of motor/generators. So like the A/C distribution
system, the conversion is non-mechanical, which vastly reduces the maintance and 
reliability of the system. Although transformers are still required to up and down 
convert the power, converting the long distance power to D/C results in an improvement
of efficency which offsets the added cost of the conversion electronics.  
  
The availability of high voltage/high power electronics also means that managing the
power distribution is vastly improved in cost and reliability as well as flexability.
 
So does that mean we will eventually switch to using D/C power from source to end-point 
as Edison envisioned? It's hard to say. But certainly not anytime soon. Far too much
of the power distribution is tied to the A/C power concept. The cost of converting
the entire A/C power distribution from source to end-point would be extreme, with
little or no gain from doing so, so there is currently no reason to make such a change. 
Tesla still wins. 

------------

How rectification works:

As a more visual description of what is happening, let's say we have a
device that uses water (our electricity analogue) to power it and an
assistant with a bucket (the rectifier analogue) to get water from the
river (the AC power source analogue). 

So, our assistant runs to the river and gets a bucket of water then 
runs back and pours the water into our water powered device. Then runs
back to the river and gets another bucket of water, repeating this 
over and over. 

The problem is that our water powered device is going to be running in 
spurts as it only gets power when the assistant pours the water into
it (which is what causes hum in the electrical circuits).            
To make the device run continuously, we need a constant source of water
(electricity). We need something to store the water temporarily. 
So we grab a bucket (the capacitor) and poke a hole in it. 
Now we have the assistant pour the water into the capacitor bucket and 
the water slowly comes out of the hole and powers our water circuit. 

By picking the right size bucket and making the hole the right size,
we can have enough water to power our water circuit while our poor 
harried assistant is rushing back and forth to the river to fill the
rectifier bucket with water and rushing back to pour it into the 
capacitor bucket. 

The amount of water and the size of the hole in the capacitor bucket 
determines how quickly the water drains out. Too small of a hole and
we don't have enough water to drive our water circuit. If we don't have
enough water in the bucket, the water going out the hole will slowly 
reduce as the pressure of the water (the voltage) behind the hole reduces. 
If the bucket is too small, we will run out of water before our assistant 
can fill it again from the rectifier bucket. 

So why not make the capacitor bucket bigger? We can, but that means that 
our rectifier bucket will need to be bigger to keep it filled. 
Our much put upon assistant might not be happy at having to carry a bigger
rectifier bucket. It will wear the poor fellow down much faster because he 
is having to carry much more water (ie electrical current) on each trip.

So how about making the hole bigger (less resistance) to make sure there 
is enough water to run the water circuit? The problem here is that we may 
run out of water in the capacitor bucket before our assistant (who is now 
thinking about finding a different job) can fill the capacitor bucket again. 

One trick is to get another assistant to help out (full wave rectifier). 
That doubles the amount of water being transferred from the river, and if 
the two assistants alternate, the capacitor bucket will be filled twice as 
often without having to make our assistant run twice as fast. 

Note: aircraft use 400Hz power, which means that we are expecting our weary 
assistant to run 6.7 times faster, so we will have to hire a strong young 
athletic type to do the work instead. But even though more expensive and
having to use specialized hardware, we can make the system smaller and 
lighter. 

Since we don't have the money to create a whole new system, plus by now
the whole town is using our old system, we have to work with what we've got.  
And we have a problem. Our water circuit is slowing down as the water level 
in the capacitor bucket drops because the pressure behind the hole in the 
bucket is going down as the water level drops and that results in a slower
stream of water coming out of the bucket. 

So over lunch we talk to our friend the fireman about the problem and he
says "Hey, you could borrow my firetruck and firehose for your experiment!
That way you could fill the bucket in no time at all!" 
That seemed like a great idea, more water to fill the bucket more quickly. 
That way we could keep it near full all the time which would keep the 
pressure of the water coming out of the hole more stable. 
So we set it up, point the firehose at the bucket and turn on the water...
and the bucket goes flying, destroying half our water circuit. 
Oh darn!  

The bucket just wasn't capable of handling that much water all at once. 
It needs to be be filled at a careful rate to keep from destroying it. 
(This is the resistance of the rectifier, or in the case of a solid state
circuit, the actual resistor in series with the rectifier). 
Of course we could get a better bucket, but that will cost lots more money, 
and firehoses aren't exactly cheap either. 

So in order to keep costs down, we try to balance the cost of the parts
with the actual needs of the circuit. 

Another trick that sometimes is used is to add a choke to the circuit. 
This would be like having our poor worn out assistant (who has just notified 
us he can't take it any more and is giving us his two weeks notice), 
instead of pouring the water into the capacitor bucket directly from the 
rectifier bucket, just gives it to another assistant who gives him an
empty bucket and sends him off back to the river. So while our soon to 
retire assistant is collecting more water, our new assistant is slowly 
pouring the water from the choke bucket into the capacitor bucket. 
This helps to keep the water level in the capacitor bucket more stable. 

If we balance it just right, the choke bucket will run out of water just 
about the time that our retiring assistant manages to struggle back from
the river with another bucket of water to give the new assistant to
replace the now empty choke bucket. The assistant then gives the empty 
choke bucket to the tired and soon to retire assistant to go fill again. 
Then once again starts emptying the new bucket of water into the capacitor 
bucket. This works great, but we do have to pay for a second assistant for 
this system to work. But it does mean that if we balance things out properly,
we can reduce the amount of water we need our overworked retiring assistant 
to drag back from the river each time, as we only need enough to keep the 
capacitor bucket near full rather than having to bring more than we need
each time to keep the bucket pressure up if we didn't have the second 
assistant there to pour more water into the bucket capacitor to keep 
it full. That means our rectifier bucket assistant doesn't have to work 
as hard, so maybe he won't quit after all. 


So, why can't we just put a bigger capacitor into the circuit? That way
it will hold more electrons and thus keep the voltage to the circuit
more stable. There are two problems that approach. One is that capacitors 
don't like having large amounts of current driven into them. If you make the 
capacitor bigger, that means that yes it will keep the voltage more stable, 
but it also means that the amount of time available to pump electrons into 
the capacitor is reduced. So we end up with a current surge into the capacitor. 
In addition, the rectifier is going to have to supply that surge, which means 
more current though it for that short duration. That means it may not help 
much, because the tube resistance determines how much current can be supplied 
by the tube. So making the capacitor bigger can quickly become a effort of
no improvement as the tube just can't supply the current needed in such a 
short time duration. 

In addition, it means that the charge current will only be pulled from the 
AC power at the peak of the curve, so you are trading time for current surge. 
This will distort the AC power and may actually cause an increase in hum 
in the rest of the circuits due to the surge caused by this approach. 
Not just because of the current surge, itself, but because of the magnetic 
field of the transformer seeing shorter pulses as the current gets pulled 
from the transformer in short bursts. This is not only reflected back into 
the AC power source, but also the magnetic field flutter can potentially be 
picked up by the rest of the tube circuits. 

The other problem is that with a bigger capacitor, when you first turn on the
circuit, the capacitor has to be charged from an empty condition. The bigger
the capacitor, the more power that is pumped into it very quickly at turn on. 
This stresses both the rectifier and the capacitor. The result is that both
will end up having shorter lifetimes because of the stress. 
So a better solution if you really want to make the voltage more stable is to
consider using a choke in the circuit instead. It is more expensive and bulky,
but it is also a more appropriate solution to the problem (assuming there 
actually is a problem). But if you are using a tube rectifier, likely in many
cases the tube resistance is enough as long as you pick the right size filter 
capacitor. 

The advantage of the choke is that it can provide power to keep the capacitor
topped off while the output of the tube rectifier is in it's off phase. 
During the charge part of the cycle, the choke builds up a magnetic field. 
While it is doing this, it also adds a bit of resistance to the circuit 
so that the charge current into the capacitor is reduced. Then during the 
time the rectifier is in the off phase, the magnetic field around the choke 
collapses. This generates electrons to feed into the capacitor to help keep 
it charged up. 

The trade off is that to work best the coke and capacitor must be tuned to 
the average current draw of the circuit, and you will still see some voltage
saging outside that range, but it is still better than a simple resistor 
in the filter as long as you don't mind having a big bulky expensive choke
and that your load on the power supply is relatively consistent. 

In some cases if you don't need a lot of current, you can consider using a 
pi filter. A pi filter is just another resistor/capacitor stage added behind 
the tube to provide added filtering. This is sort of like what the choke 
does, except it is smaller and cheaper to implement. The trade-off being that
it is not quite as good or efficient as the choke method. You can also use
a choke in the pi filter instead for greater efficency, although at greater 
cost and bulk.

Well, Our poor worn out assistant has left us, so we need to find a new one.
Unfortunately nobody in the village wants the job. So we need to come up 
with a different method to fill up the capacitor bucket. The only thing that
comes to mind is our friend's fire hose (ie a solid state rectifier). 
So maybe if we build a stronger capacitor bucket the system will survive. 
That is how modern power supplies do it without having to add resistors or 
chokes to the power supply. They just use more expensive capacitors that 
can handle the higher current peaks that occur with the solid state rectifiers. 

As an interesting side story, early in the 21st century (around 2003 to 2006), 
a company stole the recipe to make high current capacitors from Nichicon 
(a Japanese capacitor company). Unfortunately the recipe they stole was 
missing a key ingredient... 

The high currents that occur in the capacitor cause hydrogen to be released 
inside the capacitor (similar to the way hydrogen is separated from oxygen 
in water with electrolysis). At lower currents this effect is minimal and 
not a problem. At high currents the gas can build up and eventually cause 
the capacitor to blowup from the pressure. The missing part of the recipe 
was the chemical that recombined the hydrogen with the electrolyte. 
Since it was missing, the capacitors from the company who had stolen the 
plans were self destructing after a short period of time. 
Depending on use, anywhere from a few months to a few years.

A lot of equipment that had used those capacitors (primarily those built 
in Asia) failed in a very short time. You can tell when the capacitor 
has failed because the top of the capacitor will be rounded instead of 
a flat top. Also in some cases, especially where the current levels were
very high, there may be a white colored coating on the capacitor. That
is the electrolyte that has escaped the capacitor after it blew up. 

On the top of the high powered capacitors you will see some lines cut 
into the metal. These are there specifically to provide a weak point 
for the capacitor to pop open should too much gas build up inside the 
capacitor. Without the cuts, the capacitor could explosively self-destruct
causing more serious damage as the capacitor case becomes a ballistic missle. 

However, back to dealing with the loss of our wayward assistant...
By using a solid state rectifier (the fire hose analogy), we can eliminate 
the need to have a filament and make the device much more efficient 
because it has a much smaller resistance (less than an ohm). 
The only thing we have to deal with is that because of the low resistance,
the solid state diode can supply much higher currents. So much so that 
even the diode itself can be damaged unless it is controlled, or at least 
a diode is selected that can handle the currents that will be encountered. 
If a resistor or choke is not used to control the current into the capacitor,
then a capacitor also must be selected that can handle the peak currents that
will occur in the circuit. 

The worst case time of the circuit is during poower on. That is the point 
where the capacitor is completely discharged, so the diode has to supply 
large amounts of current to the capacitor during the first sinewave or two 
when power is switched on.  The amount of current is determined by the 
internal resistance of the capacitor, the internal resistance of the diode
and the internal resistance of the power transformer. If more current 
occurs than any of the parts can handle, the power supply may fail. 
This is why it is common for equipment to fail most often when power is
first applied. That is the moment of highest stress.

Once the capacitor reaches full operating charge, the current demand is 
usually much less, however it will still be "peaky", meaning that unless
a choke is used, the current will only be supplied to the capacitor
during the peak parts of the AC power waveform. How much of the peak 
current is used depends on how much the capacitor needs to be recharged 
and the resistance of the various parts of the power supply circuit.  
 
While the simple rectifier/capacitor circuit works well for most things, 
for some circuits it is still not good enough. 

The village people have been using our water power system for a while 
now and have started to build more complex devices that use the water. 
But now are complaining that the water pressure is not stable enough. 
So you hire a new assistant to man the valve (a voltage regulator) you 
installed on the hole in the capacitor bucket. His job is to keep the 
water pressure stable by adjusting the valve to keep the water in a glass 
column the same level all the time. 

There are three types of voltage regulators. A shunt regulator (gas tube 
voltage regulator or zener diode), a series regulator (sometimes referred 
to as a linear voltage regulator) which is more common, and a switching 
regulator which is becoming more common as it is the most efficent type
of regulator (but with it's own issues to deal with). 

The shunt regulator works by having the maximum amount of water (current) 
flowing out of the power supply plus a little bit more. The shunt regulator 
diverts any unused water (current) away from the rest of the system. In our 
water system, this would be like having the valve installed on the capactor 
bucket dump any excess water on the ground. In an electrical circuit we just 
dump the extra current as waste heat. The method is not very efficient and 
rather wasteful, but for low power, low cost circuits it can sometimes be the 
simplest and most effective solution.  

The series regulator is like a normal water valve such as the one that you 
use to control the water flow in your sink or shower. The series regulators 
are one of the more commonly used and have been in use for many decades. 
They particularly came into major use with the solid state circuits which
often require larger amounts of current and very stable voltages.  
A simple water pressure management version would be to install a float 
in the column of water being used to monitor the water pressure and attach 
the float to the valve so that it causes the valve to be opened wider
or narrower to keep the column the same level. We're still dumping the 
excess water on the ground, but it is under tighter management and 
we can change the water pressure more easily by changing how the 
float controls the valve. So it still is not very efficient, but it is more
efficent then the shunt regulator, especially if the demand for water 
is highly variable but we still need to maintain the same water pressure. 

The switching regulator is the most efficient way to regulate the 
water/voltage. In this case, we replace the valve with a shutter that can 
be opened or closed very rapidly. We have our assistant watch the water 
column very carefully. When the water pressure starts to rise, we have 
him immediately close the shutter. When the water pressure starts to fall, 
we have him immediately open the shutter. The advantage of this system is 
that we don't waste water by dumping it on the ground. Only a little bit
is used by our assistant when he gets thirsty. So the system is highly 
efficent. There is a down side though. That opening and closing causes the 
water to pulse through the pipes. That can make them ring similar to how
you can sometimes hear the water pipes in your home go clunk when you 
open or close the water valve to your sink. 

To some extent the distributed capacitance in the circuit will dampen this 
out, but not completely. Plus the switching regulator actually needs the 
voltage to rise and fall a bit in order ot know when to open or close the 
valve. For most digital circuits this is not a problem as they are designed 
with an expectation of some circuit noise and can ignore it. 
However for sensitive audio circuits it might not be good enough. 
So what is done is that a low drop out series linear regulator is installed 
after the switching regulator to even out the voltage. Since the series
regulator only has to deal with a very small variable voltage, the amount 
of wasted energy is much smaller than would be the case if it had to regulate 
the original voltage from the power supply. 

There is a downside to switching regulators. As well as the current surges that 
have to be delt with, they generate higher frequency wideband noise in the circuits 
that can create problems, especially with audio circuits. So a switching 
regulator is not always the best solution even though they can be the most 
efficent solution to power regulation. 
They are also more complex which can make them more expensive. 
It also means there are more parts that can break which means they have a shorter
life expectancy. Although the greater efficiency can make them worth the added 
expense, and the life expectancy of electronic components have improved a lot 
in the last few decades. A well designed switching regulator can often last
the life of the device for which it is providing power.
In addition, the greater efficency means they produce less heat which means that 
often the overall size of the device is reduced since there is less need to provide
the needed space to dump waste heat and less heat means less thermal stress on the
device, which usually translates into a longer life for the components. 
It also means less water (electricity) is used which can be a cost savings. 

In the terms of our water device, think of what it would take to design a 
device that moniters the water pressure column float and convert that to a 
device that amplifies the changes in water level monitored by the float to 
open and close the shutter valve rapidly to maintain the water pressure. 
We've replaced our generic human assistents with specialized water management 
equipment. That allows our poor tired assistent to find more productive work.

So our townspeople are happy. They have a stable water pressure and minimal 
waste of the water, which is important as the town is growing and more and 
more water usage is being demanded from the limited water supply. 
And since we can't seem to find any more assistents to manage our water 
pressure system, the automated float control has solved that problem. 
So everbody is happy.
 
Also see the companion files:
http://www.fourwater.com/files/fullrect.txt
http://www.fourwater.com/files/voltreg.txt
http://www.fourwater.com/tubeinfo.htm

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