Explainations and Formulas to Circuit Diagrams

At this web page I've explained strange expressions and connections to my circuit diagrams. To get a
better survey, I've used all expressions and names. All units are used in calculations. At the other
web pages may units have been omitted, to get an easier way to follow the calculation.

A circuit of direct current

An example of DC circuit, 1

The above diagram shows the first part of a direct current circuit. You connect a voltage of 230 volts
(V) to this circuit. The voltage is the main supply (mains) voltage, that is transformed to AC 15 V,
rectified and finally glossed.
6 (13) VA means:  all of the circuits or the whole device is taking maximum 6 volt-amperes (VA).
13 VA is the maximum input power of transformer.
50 Hz means:  the main supply frequency.
T63 mA is a slow-blow fuse of 63 mA and "T" is from the Swedish word "trög" that means "slow". ("F" is
from the Swedish word "flink" that means "fast"). In the following part you'll determine the value of
fuse by using the input current of transformer (Iin).

Formula:  Iin = Sin / Vin,  Iin < IN < (Iin X 1.5)

Example:  Vin = 230 V, Sin = 13 VA => Iin = 13 VA / 230 V <=> Iin = 0.057 A  => IN = 63 mA

R1 is the resistance of primary coil of transformer.
The greek letter 'n' (pronounced "eta"), right below the symbol of transformer, is the efficiency of
the transformer.

Example:  n = 0.6 means the efficiency of transformer is 60 %. Values of efficiency of transformers

15 (19) V means: 15 V is the normal minimum voltage from output of transformer and 19 V is unloaded
voltage of transformer.
8 VA is the maximum output power of transformer.
R2 is the resistance of secundary coil of transformer.
R2K is a short circuit resistance of transformer output. R2K is a tool to show how much the voltage
will drop at a specific load.

Formula:  R2K = R2 + ((Vout0 X Vout0) / (Vin X Vin)) X R1

Example:  R2K = 3 ohms + [(19 V X 19 V) / (230 V X 230 V)] X 480 ohms <=> R2K = 6.3 ohms.

Suppose we want to know the value of Vout at a particular current Iout.

Formula:  Vout = Vout0 - R2K X Iout

Example:  How much will the output voltage of transformer (Vout) be at the maximum output current?
          At first we calculate the maximum current IoutN. IoutN = SoutN / VoutN => IoutN = 8 VA / 15 V
          <=> IoutN = 0.53 A. Iout = IoutN. Vout = 19 V - 6.3 ohms X 0.53 A <=> Vout = 15.7 V.
          The integer of 15.7 V is 15 V and that is of course the normal minimum voltage VoutN.

4 X 1N4007 are four rectifying diodes that all are connected in a Graetz bridge.
1470 µF 35 V is an electrolytic capacitor with a capacitance (C) of 1470 micro Farads and works up to
the maximum direct voltage of 35 volts.
20 (26) V means: 20 V is the voltage when output of the device is connected to a load. This is also
momently the highest voltage when the capacitor is top-charged. 26 V will appear when there is abso-
lutely no load after the glossing capacitor, i.d. to the right of capacitor. The dot or mark below
"20 (26) V" means 20 (26) V is the valid information of this dot.
5 % ripple voltage means: the moment voltage across capacitor drops 5 percent of 20 V, i.d.
0.05 X 20 V = 1.0 V. This happens when the output voltage from transformer is momently lower than
capacitor voltage. Half of the voltage drop across capacitor gives the (minimum) measureable average value: 20 V - (1.0 V / 2) = 19.5 V.

More about the ripple voltage U:

Different voltages in the first part of the DC circuit

The red-framed area has been magnified:

The ripple voltage

The capacitor voltage is an overlayed direct voltage with a saw-toothed shaped alternating voltage and
you can hear the alternating voltage as a buzzing sound from a loudspeaker (mains zoom). Because the
t ("delta t") - range is practically lineary, the following formula can be used:

Formula:  C = (I X t) / U

Example: The capacitance C will be determined:

According to the circuit diagram above an equation system of two unknown variables can be solved and
you'll get this: Vout = 17.7 V and Iout = 0.203 A. In the next step you've the connection:
I = Iout X 0.9 => I = 0.203 A X 0.9 <=> I = 0.18 A.
I've experienced during the years that t is between 5.0 and 8.5 ms. A weight average is 8 ms.
5 percent ripple voltage means the ripple voltage drops 1 volt. We insert our values in the formula

C = (0.18 A X 0.008 s) / 1 V <=> C = 1.44 X 10-3 F. We shunt a 1000 µF - capacitor with a 470 µF -
capacitor. But it's more realistic to use a capacitor of the standard value: 2200 µF.

The final part of the DC circuit:

An example of DC circuit, 2

Resistance values in circuit diagrams are both written with or without the unit "ohms". E.g. "33k"
means 33 kilo ohms. If the power value of resistor is omitted, the maximum power is 0.6 watts (W).
U:  12,3 V means: 12.3 volts has been measured in the nearest dot or mark. An electric current value
has been measured and written at a current arrow.
The component that is to the bottom and left in the circuit diagram above, is a zener diode. It has
got 12 volts as the zener voltage and works by 5 milli amps (5 mA).
The dot (point) C1 is a "Connection Point 1" and its function is of course a connection identifi-

fg = 65 Hz means: the cut-off frequency is 65 Hertz that is determined by the capacitor 100 nF and a
network of resistors. This low-pass filter will reduce disturbances.
µA741 ("Micro Amplifier 741") is a very common operational amplifier. The numbers beside the symbol
are pin numbers of the component. A mark on the IC is located at pin number one. If there is a notch
of the case, the mark is to the left and pin no. 1 is below.

BD135 is a power transistor and is regulating the output voltage.
Pf = 2,3 W means: maximum power dissipation is 2.3 W. Rule of thumb: if Pf > 0.5 W, you're recommended
to use a heat sink.
Rthh-a = 18 K/W means: the thermal resistance of heat sink is 18 Kelvin per watt. It also has the unit:
[ECB] means: emitter, collector and base. The order is viewed by the front side of transistor.
hFE = 130 means: the DC forward current gain of transistor is 130.

5 - 16 V is VoutDC. You're able to get an output direct voltage between 5 and 16 volts.
Rut = 0,3 ohm means: the output resistance of device or circuit is 0.3 ohms. Unfortunately the output
resistance is 2 ohms at 16 volts.

Assume you want to know how much the output voltage is dropping at load. In this case you can use the
battery formula. Especially to calculate the terminal voltage, Vp.

Go to The Internal Resistance of Batteries

Example:  At first you set the output voltage to 16 V and then connect a load to the terminal.
          The output current IL is 0.17 amps. What is the output voltage VoutDC at this load?

Battery Formula:  Vp = E - Ri * IL.

In the same way the formula can be written like this:  VoutDC = VoutDC0 - Rout * IL. =>
VoutDC = 16 V - 2 ohms * 0,17 A <=> VoutDC = 15,66 V. If you round this value into a value of 2 digits,
you'll still get 16 volts.

Electrical Engineering