Chapter 0   Electrical Fundamentals.

Kirchhoff's current law states that the algebraic sum of all currents flowing into a node is equal to zero.

The consequences of these laws for series circuits are a) the sum of all voltage rises is equal to the sum of all voltage drops, and b) the current anywhere in a series circuit is equal to the current anywhere else in the same circuit.

The consequences of Kirchhoff's laws for parallel circuits are a) the sum of all upward flowing currents is equal to the sum of all downward flowing currents, and b) the voltage across any element in the circuit is equal to the voltage across any other element in the same circuit.

Ohm's law states the relationship between voltage, current and resistance in an electric circuit.

To properly apply Ohm's law it is necessary to use the resistance of a particular resistor, the current through that same resistor and the voltage across that same resistor.

When resistors are connected in series the total resistance is

When resistors are connected in parallel the equivalent resistance is

The ideal (Thevenin) voltage source is equal to the no- load output voltage of the original network.

The Thevenin resistance is equal to the resistance looking in at the terminals of the original network with all voltage sources replaced by shorts and all current sources replaced by opens.

Example 0.1.

Determine the Thevenin equivalent circuit of the network of figure 0.2.

Solution:

With no load connected to the output, there will be no voltage drop across R3. Therefore, the voltage across R2 will be the same as the output voltage. R1 and R2 make up a voltage divider. By equation 0.4 we have

V_o = 48 v x 1 k ohm / (3 k ohm + 1 k ohm ) = 12 volts.

RC Time Constant.

T is the time required for a charging capacitor to charge up to 63.2 percent of its final voltage or for a discharging capacitor to discharge to 36.8 percent of its starting voltage.

Theoretically a capacitor will never get fully charged or discharged. As a matter of practicality a capacitor is considered to be fully charged or discharged after 5 x T seconds have elapsed.

A capacitor is an open circuit for DC but has reactance for AC. The reactance of a capacitor is

An inductor has a very low resistance for DC (ideally zero) but has reactance for AC. The reactance is given by

The ripple output from a full-wave rectifier power Supply operating on 60 Hz is given by

A transistor has three terminals. They are called emitter, base and collector. Internally the transistor is made up of three alternating layers of semiconductor material, for example, NPN. The emitter is one of the N layers, the base is the P layer and the collector is the other N layer. This means that there are two P-N junctions, one between the emitter and base and the other between the collector and base.

The normal way of biasing a transistor is to forward bias the base-emitter junction and reverse bias the collector-base junction. For an NPN transistor this means to connect a current source between emitter and base so as to run current into the base, and connect a Thevenin circuit between emitter and collector such that the collector is positive and the Thevenin voltage source is greater than 0.6 volts. Figure 0.7 shows the biasing circuit.

If V_CE = 0.1 volts, the transistor is said to be in saturation. If V_CE = V_TH the transistor is said to be in cutoff. If 0.1 volts < V_CE < V_TH is true, the transistor is said to be in linear operation.

When the transistor is in linear operation the collector current is controlled by the base current. If the base current is zero, the collector current is zero because the collector base junction is reversed biased. As base current increases, the collector current increases. The current gain of the transistor is defined as follows.

Common Emitter Amplifier.

If the emitter bypass capacitor is removed the gain becomes

The input resistance is R_in in parallel with R_B. R_in is given by

The upper frequency limit of an amplifier is considered to be the frequency at which the output is 3 db down from the output at medium frequencies. This is variously known as the upper frequency limit, the upper 3 db frequency, the upper corner frequency, the upper cutoff frequency or the bandwidth. We will symbolize this frequency by f_C.

The Miller effect causes the input capacitance of an inverting amplifier to be much larger than the stray wiring capacitance. The Miller capacitance is given by

Common Collector (Emitter-Follower) Amplifiers.

The input impedance of this circuit is the parallel combination of R_in in parallel with both R₁ and R₂.

The output impedance of this circuit is R_E in parallel with R_OUT.

Because the voltage gain is very close to + 1, equation 0.22 tells us that the Miller capacitance CM is essentially zero. Do not get the mistaken impression that the input capacitance is zero. There is always stray wiring capacitance.

Common Base Amplifier.

A common base amplifier is noninverting. Equation 0.22 would actually give a negative input capacitance. This negative Miller capacitance will cancel with positive (real) stray circuit capacitance and it is possible to achieve a net zero input capacitance. Such an amplifier can have a very wide bandwidth.

Common base amplifiers are used as amplifiers in VHF and UHF receivers and as wide-band amplifiers in the vertical channel of oscilloscopes. When used in this application the power supplies are arranged so the base is at DC as well as AC ground. This permits a low impedance ground connection.

Feedback.

A differential input consists of two inputs with respect to ground. If the same signal is applied to both inputs, the difference between the two inputs will be zero and the output of the amplifier will be zero, theoretically. There will be some small output. If two signals which are similar but not identical are applied, the amplifier will amplify the difference between the two signals.

If one input is grounded and a signal put into the other input, the amplifier will amplify that signal. If the signal is put into the noninverting input, the output will be of the same sign as the input signal. If the signal is put into the inverting input, the output will be of the opposite sign as the input signal.

If the inverting input is more positive than the noninverting input, the output will go negative. If the noninverting input is more positive than the inverting input, the output will go positive.

When we analyze operational amplifier circuits, the feedback is always assumed to be negative. The equation which results is

Equation 0.26 is seldom seen in connection with op amps because the open loop gain A is so large. The limit as A approaches infinity is,

Equation 0.27 is based on the assumption that A x B is much greater than one. A x B may not always be much greater than one, especially at high frequencies.

The gain of an op amp falls off as frequency increases at the rate of 20 db per decade. The unity gain frequency of an op amp is given in its specifications. The gain A at any frequency f is given by

In the case of a 741 op amp which has a unity gain bandwidth of 1 megahertz, the gain at 20 kilohertz is only 50. Common emitter amplifiers often have more gain than this.

If the gain is low due to frequency effects, equation 0.26 should be used instead of equation 0.27.

Figure 0.13 is the circuit of an inverting amplifier. For this circuit the value of B is given by

Power Supply.

In most cases the power supply is symmetrical. For example plus 12 and minus 12 volts DC. This is often abbreviated +/- 12 V. If the writer is working with a sophisticated word processor the mathematical symbol with a plus sign above a minus sign will be used. There are some special op amps that have been designed to operate from a single supply but these are not often used. Also on rare occasions a designer may contrive to operate a symmetrical supply op amp from a single supply. This is generally not considered to be good engineering and is very rarely found in commercially manufactured equipment.

Junction FET.

When the P-N junction of the Gate and channel is reversed biased a depletion region in the channel reduces its effective cross section area. This restricts current flow between the Source and Drain. The larger the reverse bias, the more the channel is restricted and the smaller the current between Source and Drain. The JFET (Junction Field Effect Transistor) is almost never used with the Gate to channel junction forward biased.

Note: In oscillators and class C amplifiers the gate is purposefully driven positive which causes rectification. The rectified voltage is negative which provides proper bias for an N channel FET. When a MOSFET is used, see below, a diode is connected from Gate to Source to accomplish the necessary rectification.

Metal Oxide Semiconductor FET (MOSFET).

The MOSFET can be made in another configuration. A lightly doped P region, part of the substraight, is placed between the Source and Drain. This does not allow conduction between them. When the Gate is biased positively the holes in the region between Source and Drain are repelled deeper into the substraight leaving electrons behind. This effectively turns this region from P to N type semiconductor which allows conduction. The more positive the Gate the more conduction there is between Source and Drain. This is known as an enhancement mode MOSFET.

In 1987 MOSFETs were used primarily for switching in logic circuits. They are still used for that but a new generation of MOSFETs has been developed which will stand up to very high voltage and power. In that respect they are as close to silicon tubes as can be or probably ever will be achieved.

A special type of JFET known as a GASFET (Gallium Arsenide) is used as the low noise amplifier in satellite receivers.

High voltage MOSFETs are used in both analog and switching modes. The former includes but not limited to, * pass transistors in constant voltage and constant current power supplies, and output transistors in audio and servo amplifiers. The latter includes * switching power supplies, and variable speed drives for industrial electric motors.

* Have you ever read one of those terms of use things on the internet?

Filament type tubes are the oldest type. In the golden age of tubes, 1950s, filament types were only used for very low power, used in portable radios, or high power, in radio transmitters. The heater/cathode type is by far the most common. They were used in radios, TV sets, audio amplifiers and a wide range of measurement and industrial equipment.

The minimum tube is a diode which consists of a cathode and anode. This is used primarily as a rectifier in power supplies and radio detectors.

Next higher is the triode, 3 element tube. (Note: The heater does not count when elements inside a tube are counted.) It consists of the cathode, control grid, and plate or anode. This type is favored by audio enthusiasts. Like the FET, the grid usually operates negative with respect to the cathode while the plate is positive.

Next higher on the totem pole is the tetrode which has two grids. The one closest to the cathode is the control grid and the outer one is known as the screen grid. The additional grid was added to serve as an electrostatic shield between the grid and plate. The control grid to plate capacitance caused RF amplifiers to oscillate and a means was needed to reduce this capacitance. The screen grid is made positive usually about equal to the plate or occasionally even higher. This type of tube has problems and very few true tetrodes were ever manufactured. There is a form of the tetrode in which a beam forming element was added between the screen grid and plate. It was connected to the cathode within the tube. This was done initially to avoid infringing on a patent but turned out to produce one of the best tubes ever made, the 6L6 and its many derivatives. The beam forming element suppressed secondary emission of electrons from the plate.

The pentode inserts a third grid between the screen grid and plate. This is also a method of suppressing secondary emission of electrons from the plate. It is called the suppressor grid. It is often brought out to a pin and the designer has to tie it to the cathode, or rarely, ground.

Toward the end of the golden age of tubes when there began to be significant competition from transistors, a type of tube was developed for use in car radios that would operate with no more than 12 volts on the plate. It was known as a space charge tube and was a pentode, but the control grid and screen grid were interchanged. The grid closest to the cathode was operated at 12 volts to get the electrons moving and the second grid was the control grid. The third grid served as a shield between the plate and control grid to prevent oscillation when the tube was used as a radio frequency amplifier.

Figure 0.15a is a triode resistance coupled amplifier. The current flowing through R_k produces a voltage drop which makes the cathode positive with respect to ground. The grid is held at ground potential by R_c so the grid is negative with respect to the cathode. This is an audio frequency amplifier. C_k filters the AC component from the cathode voltage which if present would reduce the gain of the amplifier. Note: Sometimes C_k is deliberately omitted which reduces distortion along with reducing the gain.

The output of this amplifier circuit appears across R_cf. R_cf is the grid resistor of the following stage. It is assumed that this amplifier stage is sending its signal to another amplifier stage.

Figure 0.15b is a pentode amplifier stage. Pentode circuits give higher gain than triodes but have a higher parts count. Biasing works the same way as in the triode circuit. C_c2 prevents reduction of the gain which would occur if AC signals were allowed to appear at the screen grid. This capacitor is never omitted. However, if the cathode bypass capacitor is omitted the screen grid bypass capacitor must be returned to the cathode instead of ground. Gain is higher and distortion lower than with C_c2 returned to ground.