23.14 SINE WAVE INVERTER
23.14.1 Operating Quality Factor Q
We start the design by defining the quality factor Q. This is an important parameter as
it sets the magnitude of the primary current and allows the core size and wire sizes to
Q defines the ratio of reactive current, which does not contribute to output power, to real
(resistive) current. Another way of looking at "Q" is that it is proportional to the ratio of
energy circulating in the tank circuit, to the energy taken away by the load each cycle.
High Q circuits have nice clean sine waves, which are maintained by the larger cur-
rents circling in the tank circuit, as the tank circuit is loaded (rather like the flywheel in a
mechanical system). This clean sine wave is obtained at the cost of high circulating current
in the tank circuit, leading to high loss in the resistance of the primary windings P1 and
P2. Conversely, low Q circuits have more distortion of the sine wave, but less loss. In this
type of self-resonating inverter circuit, a compromise value will be found with a Q between
2 and 5.
Since the ac voltage across the capacitor C2 tends to remain constant, the value of C2
and the frequency tend to set the reactive current and hence Q. (The larger C2, the higher
the Q). This is explained more fully in the supplementary section Part 4, Chap. 2.
In this example C2 is 1000 pF, the frequency is 50 kHz, and the RMS voltage of the tank
circuit is 477 volts. We can calculate the reactive current as follows:
At 477 volts RMS the current will be
477 3180 150
The effective input current reflected to the primary is
20 477 42
The working Q will be
150 42 3 .6
T1 provides two functions. First, it is a transformer, stepping down the 477-V RMS primary
voltage to the required secondary voltage of 20 volts RMS. The primary windings P1 and
P2 and the effective core permeability form the resonating inductor, and C2 the resonating
capacitor in the parallel tank circuit. These are chosen to set the natural resonant frequency
to 50 kHz.
The preferred design approach is to select C2 for the required Q (see above). The core
gap is then adjusted, to get the effective permeability of the core for the correct inductance,
so that P1 in series with P2 will resonate at 50 kHz with the selected capacitance C2.
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23. AUXILIARY SUPPLY SYSTEMS
Tip: In general with ferrite cores, providing the core size is not too small, it will be found that
when the minimum primary turns (as defined by the frequency and primary voltage) have
been calculated and wound, the inductance of the primary will be too high. Hence, a core
gap will normally be required to reduce the effective core permeability and inductance. This
is convenient, because it allows the inductance to be adjusted for optimum performance by
simply adjusting the core gap. (If the inductance is too low, increase the primary turns).
23.14.2 Primary Voltage
It is shown in Part 4, Chap. 2 that the voltage across the tank circuit (the primary voltage
across P1 and P2) is well defined and for our purpose here, we can assume that the peak
voltage will be near P Vin.
In this example:
P(215 VDC) 675 volts peak. (Fig. 1.23.9 (B)).
The RMS value will be
In this example:
(675)0.707 477 volts RMS.
Note: The "on" state overlap on Q1 and Q2 will increase this voltage by about 10%.
23.14.3 Core Size
The working "Q" (quality factor of the tuned circuit, Section 23.14.2) defines the ratio of
reactive current to real (primary) load current. To find the primary current, we can use the
reactive current I
flowing in the resonant capacitor C2, and the real current I
into the primary from the load.
A Q of 3.6 was used to provide a good sine wave and optimum waveforms. However, the
primary current in P1 and P2 will be almost four times larger than it would be in a non-
resonant system, (the reactive component does not contribute to the output power but does
cause heating in the primary winding). Hence for our 20-watt sine wave system, we would
choose a larger core, In this example we use a core recommended for a 60 watt system.
Hence in this example an ETD 35 was chosen.
23.14.4 Calculating Primary Turns
The ETD 35 has a core area of 92 mm2.
As shown above in a sine wave system, the primary turns may be calculated as follows:
Minimum primary turns
Winding voltage (Volts RMS)
f Frequency (Hz)
B Flux density (Tesla, typ. 150 mT)
Effective core area (mm2)
In this example
It was found convenient to wind 6 layers of 28 AWG at 35 turns per layer (with a center tap
at three layers), giving a total of 210 turns with a tap at 105 turns.
(This is acceptable, because the increased turns reduce the flux density to 111 mT,
reducing core loss).
23.14.5 Turns Ratio (Primary to Secondary)
The primary voltage is 477 volts RMS and the secondary is required to be 20 volts RMS
so the ratio is:
23 9 1
so the secondary will require
23.14.6 Core Gap
With the frequency ( f
50 kHz) and resonant capacitor (C2 1000 pF) defined, the
required resonating inductance (L
) may be calculated.
With the primary turns defined and the core size and permeability known, the core gap may
be calculated. (See Part 3, Chap. 1.10.5)
However, I find it much faster to simply adjust the gap to get the required frequency in
the working prototype as follows:
Start with a small core gap (say 0.010 inches) and hold the cores in place with an elastic
band. Then apply sufficient input voltage for oscillation and check the frequency. Adjust
the gap for the required frequency, and note the gap size.
Note:A "butt gap" is preferred. (That is, a gap the goes right across all three legs of the EE
core). In this example a butt gap of 0.018 inches was required for 50 kHz operation. A butt
gap reduces the local heating caused in the windings due to gap flux fringing. Cores that
are gapped in the center pole only will have considerable local fringing that will cause eddy
current heating in nearby windings. (See construction details in Part 4).
23.14.7 Calculating the Turns for the Drive Winding S1
Good regenerative starting will be found with peak drive voltages between 6 and 10 volts.
The primary volts/turn 477/210 2.3 volts per turn, so 3 turns will give 6.8 volts RMS,
(9.6 volts peak) and this was used in the prototype shown here.
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23. AUXILIARY SUPPLY SYSTEMS
23.15 REDUCING COMMON MODE NOISE
With the choke located in the L1 position, in series with the center tap of the 50-kHz
transformer, the 100-kHz 337-V haversine peak voltage (Fig. 1.23.9 trace (B)) will
capacitively couple to the 20-volt sine wave output winding, introducing common
Moving L1 to the alternative position LA in the common return of the DC supply (this
does not change the function of the circuit) has the advantage that the center tap now has a
DC voltage on it, and the common mode injection point is removed.
Although the function is unchanged, the waveforms will look quite different.
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Stabilized-voltage power supplies, both switching and linear, have extremely low output
resistances, often less than 1 m7. Consequently, when such supplies are connected in
parallel, the supply with the highest output voltage will supply the majority of the output
current. This will continue until this supply goes into current limit, at which point its
voltage will fall, allowing the next highest voltage supply to start delivering current,
and so on.
Because the output resistance is so low, only a very small difference in output voltage
(a few millivolts) is required to give large current differences. Hence, it is impossible to
ensure current sharing in parallel operation by output voltage adjustment alone. Generally
any current imbalance is undesirable, as it means that one unit may be overloaded (operat-
ing all the time in a current-limited mode), while a second parallel unit may be delivering
only part of its full rating.
Several methods are used to make parallel units share the load current almost equally.
24.2 MASTER-SLAVE OPERATION
In this method of parallel operation, a designated master is selected, and this is arranged
to provide the voltage control and drive to the power sections of the remainder of the
Figure 1.24.1 shows the general arrangement of the master-slave connection. Two
power supplies are connected in parallel. (They could be switching or linear supplies.)
Both supplies deliver current to a common load. An interconnection is made between the
two units via a link (this is normally referred to as a P-terminal link). This terminal links
the power stages of the two supplies together.
The master unit defines the output voltage, which may be adjusted by VR2. The slave
unit will be set to a much lower voltage. (Alternatively, the reference will be linked out,
LK1.) The output of amplifier A1` will be low, and diode D1` is reversed-biased. Q3` will
not be conducting, and the drive to Q2` will be provided by Q3 in PSU1 via the P-terminal
link. The drive transistor Q3 must have sufficient spare drive current to provide the needs
of all the parallel units; hence there is a limit to the number of units that can be connected
in parallel. Drive accommodation is normally provided for a minimum of five parallel
In this arrangement, the slave supplies are operating as voltage-controlled current
sources. Current sharing is provided by the voltage drop across the emitter sharing resis-
`. The current-sharing accuracy is not good because of the rather variable
base-emitter voltages of the power transistors. A sharing accuracy of 20% would be typical
for this type of connection.
The major disadvantage of master-slave operation is that if the master unit fails, then
all outputs will fail. Further, if a power section fails, the direct connection between the two
units via the P terminal tends to cause a failure in all units.
24.3 VOLTAGE-CONTROLLED CURRENT
This method of parallel operation relies on a principle similar to that of the master-slave,
except that the current-sharing P-terminal connection is made at a much earlier signal
level in the control circuit. The control circuit is configured as a voltage-controlled current
source. The voltage applied to the P terminal will define the current from each unit, the
total current being the sum of all the parallel units. The voltage on the P terminal, and hence
the total current, is adjusted to give the required output voltage from the complete system.
Figure 1.24.2 shows the general principle.
In this arrangement the main drive to the power transistors Q1 and Q1` is from the
voltage-controlled current amplifiers A1 and A1`. This operates as follows.
Assume that a reference voltage REF has been set up by one of the amplifiers. (REF2
and REF2` must be equal, as they are connected by the P terminals.) The conduction of
FIG. 1.24.1 Linear voltage-stabilized power supplies in master-slave connection.
24. PARALLEL OPERATION OF VOLTAGE-STABILIZED POWER SUPPLIES
transistors Q1 and Q1` will be adjusted by the amplifiers so that the currents in the two
current-sensing resistors R1 and R1` will be well defined and equal. The magnitude of the
currents depends on the reference voltage on P and the resistor values.
The dominant control amplifier, A2 or A2` (the one set to the highest voltage), will now
adjust the current to obtain the required output voltage. The other amplifier will have its
output diode reverse-biased.
The major advantage of this arrangement is that a failure in the power section is
less likely to cause a fault in the P-terminal interconnection, and the current sharing
is well defined.
This circuit lends itself well to parallel redundant operation. See Sec. 1.24.5.
24.4 FORCED CURRENT SHARING
This method of parallel operation uses a method of automatic output voltage adjustments
on each power supply to maintain current sharing in any number of parallel units. This
automatic adjustment is obtained in the following way.
Because the output resistance in a constant-voltage supply is so low (a few milliohms
or less), only a very small output voltage change is required to make large changes in the
output current of any unit.
With forced current sharing, in principle any number of units can be connected in paral-
lel. Each unit compares the current it is delivering with the average current for all units in
the total setup and adjusts its output voltage so as to make its own output current equal to
the average current.
Figure 1.24.3 shows the principle used for this type of system. Amplifier A1 is the
voltage control amplifier of the supply. It operates in the normal way, comparing the
output voltage from the divider network R3, R4 with an internal reference voltage `V
and controlling the power stage so as to maintain the output voltage constant. However,
FIG. 1.24.2 Parallel operation of current-mode-controlled linear power supplies, show-
ing natural current-sharing ability.
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