## 1.1.16

Basic mains wave forms. The above sketch shows the basic ac wave forms you
should understand where ac voltage levels vary positively and negatively when
referenced to 0V, the earth or ground reference voltage potential.
There are two wires coming into your house from the mains.
One is black, and called the "neutral" wire and is connected to ground at the
house circuit distribution board via an earthing to copper water pipes or a copper
clad stake buried in the ground and the voltage on the black is almost zero volts
in reference to earth.
The green yellow insulated wire in the 3 wire cables around a house are all joined
to the water pipe or stake connection.
The other wire is called the "active" because its voltage is moves to + 340V peak to
-340V peak at a rate of 50 Hz  and the graph of such waves is shown above as
approximate sine waves.
The active and neutral wires are connected to a circuit breakers or fuses and then
to the 3 wire cables for power and lighting.
Each wire in the cable has red insulation for active, black insulation for neutral and
green+yellow for the earth wire in Australia.
Appliances which require  their cases to be connected to earth directly  can be
accommodated such as washing machines, but the energy carrying circuit is via
the red and black wires.
In the US the mains active is about 110Vrms, and has F = 60Hz.
In Fig 1 the top waveform X is the incoming mains single phase of ac wave
applied to the transformer primary.
The single secondary shown at left shows the wave form X also occurring.
The top left transformer is supplying AC power only to the load resistance
which could be a heater filament in a tube. No rectified dc currents flow, only ac.
It is impossible to power signal circuits with AC since the ac signal would swamp
any signal we tried to have.
Rectified wave forms,
The middle waveform shows the ac wave X shown again, but with the ripple
wave form that appears at the top of RL1, and C1. When the positive going voltages
of the ac wave go higher than the voltage in the cap C1, the diode can conduct current
in the direction of the "arrow" and the the cap is charged up to the peaks shown in the
ripple voltage wave. But no sooner does the cap get charged up and the ac wave
potential reduces and travels negatively, and the cap tends to discharge its store of
energy through RL1 much more slowly than the ac wave goes negative, so then the
ac wave voltage is less than the cap voltage and current cannot flow in the diode in
the opposite direction of the arrow, so while the ac voltage is negative the cap voltage
stays relatively positive with respect to 0V.
Bath water?
Rectifying is the converting of alternating voltage to a single polarity voltage and is
like a like a guy filling a bath with water by tipping a bucket full in at each positive
wave crest, but the bath is losing a steady flow of water out the plug hole as he fills
the bath. The water running out is like the Resistive Load connected to every power
supply.
The average bath water level is like the dc voltage level at half way between the peaks
and troughs of the ripple wave form. And so we have a dc voltage level in C1, but there
is small ac wave as shown also superimposed upon the dc level. The flow in RL1 is
mainly a DC flow, but because some ripple voltage is present at the top of the capacitor,
there is some small ac ripple current in RL1, and its frequency is the same as the ac wave
form X, or mains frequency of 50 or 60 Hz. The ripple voltage contains many harmonics
of the mains basic frequency. The current flow in the diode is shown in a hatched wave
below positive peaks in the ac voltage wave. The current only flows in the diode for a
small fraction of the ac wave form; the current flow is like bucket fulls of water being
tipped into the bath, and the peak charging current into the cap through the diode must
be higher than the ripple current measured with an rms meter, since the input charge
current x time must transfer the same energy into the cap as flows out of the cap into
the load RL in the form of Vdc x current x time. The set up as shown in the middle
transformer with R1, C1 is a half wave rectifier, since only the positive going 1/2 of
each the ac wave is converted to a DC flow.
The lowest set of waves show wave X and wave Y with the ripple wave at C2, R2.
In the transformer at bottom left the secondary has two windings arranged so equal turns
exist each side of where the two windings join, which is called a centre tap. Each winding
has the same turns as the half wave rectifier transformer winding. Wherever you have a
winding with a CT taken to 0V, the ac signals at each free end are of opposite phase
and 180 degrees out of phase with each other. The result is that "balanced output
voltages" exist at each free end of the two windings. There are also two diodes, and as
each wave goes positive there are alternating XYXYXY charging pulses at twice the
mains fundamental frequency of 50 or 60Hz. This arrangement is called a full wave
rectifier, and is very common in tube amps which use a tube rectifier which contains
two diodes with a commoned cathode. When silicon diodes were invented, bridge
rectifiers and voltage doubler arrangements which are shown in textbooks were rapidly
adopted because they offered much greater efficiency, lower cost and far better voltage
regulation.
Diode resistance,
Tube rectifiers have considerable series resistance often above 50 ohms when conducting
current and thus dissipate heat during their function, so the tube gets quite hot as a result.
There are strict limitations on the capacitance value in uF so that peak currents do not
exceed the cathode current ability. Silicon diodes have very low "on" resistance of only
about 1 ohm and a 1N5408 can easily take 3 amps or more than 10 times the current
rating of a tube rectifier. So Si diodes tend to run cool because the heat loss is low.
Heat =
I squared x R. Because Si diode "on" resistance is so low the power supply
output voltage regulation with load current change is far better than with any tubed
rectifier power supply, and the larger current ability allows for large value electrolytics
to be used and the peak charging currents are then limited by the winding resistances
and not the diode "on" resistance.
Because peak charge currents in silicon diodes are much larger than tube rectifiers some
say there is a noise problem since power supply noise can all too easily find its way into
earth paths and feedback wires by magnetic induction or other leakage or voltage
generation in low impedance earth buss wires.
I have found that with careful design and wire layouts such noise problems never arise.
If we assume that R1 = R2, and that C1 = C2, and that the ac voltage in the half wave
rectifier winding is the same as the voltages in each half of the balanced winding, then
the dc output voltage will be slightly higher with the balanced set up because the rate
of discharge of C2 is about the same as C1, but C2 is charged twice as often as C1,
so in fact the dc voltage in C2 is slightly higher, and the ripple voltage is about 1/2
the value of that across C1. In other words, the full wave rectifier is more efficient
than the half wave rectifier.
Ripple voltage and output dc voltage vs C and Idc.
In all the above rectifiers, the higher the value of C, the less ripple voltage you get for
a given dc current output, and the closer the dc voltage output becomes to the peak
ac voltage at the winding. Or you an say the lower the dc current output for a given
value of C, the less ripple voltage is present, and the higher the dc voltage approaches
to the peak ac voltage from the winding.
The maximum dc voltage that can exist in a cap being charged by an ac wave is the
the peak voltage of the ac wave form when there is no load to drain out the voltage
in the cap. So all caps in the power supply should be able to easily withstand
1.41 x the Vrms of the HT winding. Thus where a 280Vrms secondary is used,
the actual Vrms could be +/- 10%, or between 252V and 308V due to mains voltages
variations; I have seen the mains here at 255Vrms on some days. Always design
the power supply to be able to cope with the HT winding being 10% higher than
the actual design centre value. Hence the rectified peak voltage with no load could
be 1.41 x 308 = +434V dc, so therefore caps should have a V rating well above 434V.
450V rated caps are easily available, but seriesed 250V or 350V rated caps would
be better.
Often the price of 470uF x 350V rated caps are much lower than 470uF x 450V rated
caps so using the 350V rated types in seriesed pairs with dividing resistors to equalize
the Vdc across each cap is not too expensive.
The mains ac wave is usually a sine wave, but harmonics do exist to make the mains
look like a triangular wave with flattened peaks. The harmonic voltages in the mains
supply are seldom more than 5% of the 50Hz or 60Hz wave and are usually all odd
numbered, mainly 3H and 5H. But for practical design purposes, the mains wave form
is considered to be a sine wave and the rms measurement of it is 240Vrms in Australia
and the peak voltage value of the wave crests is 1.414 x Vrms = 339.4V.
With a given secondary winding the Vdc will reach a peak value of nearly 1.41 x Vrms.
As we drain more and more current to a load from the input cap the dc voltage tends to
drop so that in an average power supply, the conversion factor from Vrms to Vdc reduces
from a maximum of 1.414 with no load to about 1.35 with Si diodes. With tube diodes the
Vdc is often only just above the Vrms value of the transformer winding voltage.
To have 600mA at +480V with tube diodes I would have to use a full wave CT winding
for the B+ with the ac voltage at about 420V-0-420V and with at least three paralleled GZ34.
The tube rectifiers could all be replaced with just two seriesed pairs of IN5408, and
capacitors could have higher values and thus the ripple voltage would be much lower.

Half wave rectifiers have their place in all sorts of circuits where load current is low
and efficiency isn't a big problem such as deriving a grid bias voltage for output tubes.
Half wave rectifiers can use 2 diodes and two caps to make a voltage doubler so
alternatively charge one cap positively, the other negatively, and with one transformer
winding end taken to the connection of the two series caps, thus giving a dc voltage
output near twice the peak ac voltage of the winding. This voltage doubler rectifier
produces a ripple frequency same as a full wave rectifier but is not quite as efficient
as a full wave type, but with silicon diodes and small sized large value modern capacitors,
this doubler is much more efficient than any tubed rectifier arrangement. The voltage
doubler arrangement allows a more efficient transformer winding with only 1/2 the turns
and 1/2 the voltage of the bridge rectifier. Or 1/4 of the turns and 1/4 of the end to
end voltage of a CT winding used for a tube rectifier. So with a doubler used in
B+ supplies, and much lower winding voltages, control relays meant for mains
voltages may be used.