ASCII control characters,Useful formulae and Time constant.

ASCII control characters

Useful formulae

Boolean algebra (laws of)

C is picofarads, K is the dielectric constant (air = 1). ¢ is the area of the plate in square cm and d the thickness of the dielectric.

Calculation o f overall capacitance with:

Characteristic impedance

where K = dielectric constant, = outside diameter of inner conductor, = inside diameter of outer conductor.

Dynamic resistance

In a parallel-tuned circuit at resonance the dynamic resistance is:

where L = inductance (henries), C = capacitance (farads), r = effective series resistance (ohms), Q = Q-value of coil, and ¤ = 2„ x frequency (hertz).

Frequency — wavelength — velocity

(See also Resonance.)
The velocity of propagation of a wave is:

v = f k metres per second

where/ = frequency (hertz) and © = wavelength (metres). For electromagnetic waves in free space the velocity of propagaP tion v is approximately 3 x 108 m s '1, and i f /i s expressed in kilohertz and © in metres:

Horizon distance

Horizon distance can be calculated from the formula:

S = 1.42V//
where S = distance in miles and H = height in feet above sea level.

Impedance

The impedance of a circuit comprising inductance, capacitance and resistance in series is:

where R =resistance (ohms), ro = 2Jt x frequency (hertz), L = inductance (henries), and C =capacitance (farads).

Inductance

Single layer coils:

If the desired inductance is known, the number of turns required may be determined by the formula:

where N = number of turns, a = radius of coil in inches, n = number of turns per inch, L = inductance in microhenries (JJH) and l = length of coil in inches.

Calculations of overall inductance with:

Meter conversions

Increasing range of ammeters or milliammeters

Current range of meter can be increased by connecting a shunt resistance across meter terminals. If Rm is the resistance of the meter: R, the value of the shunt resistance and n the number of times it is wished to multiply the scale reading, then:

Increasing range of voltmeters

Voltage range of meter can be increased by connecting resistance in series with it. If this series resistance is R, and Rm and n as before, then:

Negative feedback

Voltagefeedback

Gain with feedback:

where A is the original gain of the amplifier section over which feedback is applied (including the output transformer if included) and b is the fraction of the output voltage fed back.

Distortion with feedback:

where d is the original distortion of the amplifier.

Ohm's law

where I= current (amperes), V =voltage (volts), and R =resistance (ohms).

Power

In a DC circuit the power developed is given by:

Power ratio

Reactance

The reactance of an inductor and a capacitor respectively is given by:

where w = 27t x frequency (hertz), L =inductance (henries), and C = capacitance (farads).

The total resistance of an inductance and a capacitance in series is XL -Xc.

Resistance

Calculation of overall resistance with:

Resonance

The resonant frequency of a tuned circuit is given by:

Time constant

For a combination of inductance and resistance in series the time constant (i.e. the time required for the current to reach 63% of its final value) is given by:

where L =inductance (henries), and R =resistance (ohms).

For a combination of capacitance and resistance in series the time constant (i.e. the time required for the voltage across the capacitance to reach 63% of its final value) is given by: