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CIRCUIT ANALYSIS: PORT POINT OF VIEW
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The elements of Fig. 1-1(d) to (h) are called active elements because each is capable of continuously supplying energy to a network. The ideal voltage source in Fig. 1-1(d) provides a terminal voltage v that is independent of the current i through it. The ideal current source in Fig. 1-1(e) provides a current i that is independent of the voltage across its terminals. However, the controlled (or dependent) voltage source in Fig. 1-1( f ) has a terminal voltage that depends upon the voltage across or current through some other element of the network. Similarly, the controlled (or dependent) current source in Fig. 1-1(g) provides a current whose magnitude depends on either the voltage across or current through some other element of the network. If the dependency relation for the voltage or current of a controlled source is of the rst degree, then the source is called a linear controlled (or dependent) source. The battery or dc voltage source in Fig. 1-1(h) is a special kind of independent voltage source.
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Fig. 1-1
SPICE ELEMENTS
The passive and active circuit elements introduced in the previous section are all available in SPICE modeling; however, the manner of node speci cation and the voltage and current sense or direction are clari ed for each element by Fig. 1-2. The universal ground node is assigned the number 0. Otherwise, the node numbers n1 (positive node) and n2 (negative node) are positive integers
Fig. 1-2
CHAP. 1]
CIRCUIT ANALYSIS: PORT POINT OF VIEW
selected to uniquely de ne each node in the network. The assumed direction of positive current ow is from node n1 to node n2 . The four controlled sources voltage-controlled voltage source (VCVS), current-controlled voltage source (CCVS), voltage-controlled current source (VCCS), and current-controlled current source (CCCS) have the associated controlling element also shown with its nodes indicated by cn1 (positive) and cn2 (negative). Each element is described by an element speci cation statement in the SPICE netlist code. Table 1-1 presents the basic format for the element speci cation statement for each of the elements of Fig. 1-2. The rst letter of the element name speci es the device and the remaining characters must assure a unique name.
Table 1-1 Element Resistor Inductor Capacitor Voltage source Current source VCVS CCVS VCCS CCCS Name R::: L::: C::: V::: I::: E::: H::: G::: F::: AC or DC
Signal Type
Control Source
Value  H F Vb Ab
AC or DCa cn1 ; cn2 V::: cn1 ; cn2 V:::
V/V V/A A/V A/A
a. Time-varying signal types (SIN, PULSE, EXP, PWL, SFFM) also available. b. AC signal types may specify phase angle as well as magnitude.
CIRCUIT LAWS
Along with the three voltage-current relationships (1.1) to (1.3), Kirchho s laws are su cient to formulate the simultaneous equations necessary to solve for all currents and voltages of a network. (We use the term network to mean any arrangement of circuit elements.) Kirchho s voltage law (KVL) states that the algebraic sum of all voltages around any closed loop of a circuit is zero; it is expressed mathematically as
n X k 1
vk 0
1:4
where n is the total number of passive- and active-element voltages around the loop under consideration. Kirchho s current law (KCL) states that the algebraic sum of all currents entering every node (junction of elements) must be zero; that is
m X k 1
ik 0
1:5
where m is the total number of currents owing into the node under consideration.
CIRCUIT ANALYSIS: PORT POINT OF VIEW
[CHAP. 1
STEADY-STATE CIRCUITS
At some (su ciently long) time after a circuit containing linear elements is energized, the voltages and currents become independent of initial conditions and the time variation of circuit quantities becomes identical to that of the independent sources; the circuit is then said to be operating in the steady state. If all nondependent sources in a network are independent of time, the steady state of the network is referred to as the dc steady state. On the other hand, if the magnitude of each nondependent source can be written as K sin !t  , where K is a constant, then the resulting steady state is known as the sinusoidal steady state, and well-known frequency-domain, or phasor, methods are applicable in its analysis. In general, electronic circuit analysis is a combination of dc and sinusoidal steady-state analysis, using the principle of superposition discussed in the next section.
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