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A simplified drawing of an NPN bipolar transistor is shown in Fig 22-1A, and the schematic symbol is shown in Fig 22-1B The P-type, or center, layer is called the base One of the N-type semiconductor layers is the emitter, and the other is the collector Sometimes these are labeled B, E, and C in schematic diagrams A PNP bipolar transistor has two P-type layers, one on either side of a thin N-type layer (Fig 22-2A) The schematic symbol is shown in Fig 2-22B It s easy to tell whether a bipolar transistor in a diagram is NPN or PNP If the device is NPN, the arrow at the emitter points outward If the device is PNP, the arrow at the emitter points inward Generally, PNP and NPN transistors can perform the same functions The differences are the polarities of the voltages and the directions of the resulting currents In most applications, an NPN device can be replaced with a PNP device or vice versa, the power-supply polarity can be reversed, and the circuit will work in the same way as long as the new device has the appropriate specifications

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which has a mean value of gb xa and Pf = cov( b (t2 )) = Ta I Given g the available information, there is no means to distinguish the correct values of gb and xa Therefore, the initial value assignments gb (t2 ) xa (t2 ) = gb (t2 ) = 0 (1064) (1065)

of an NPN transistor At B, the schematic symbol Electrodes are E = emitter, B = base, and C = collector

are a design choice which has the correct mean value (ie, gb (t2 ) xa (t2 ) = gb (t2 )) and corresponds to the expectation that the dominant initialization error will be due to attitude not accelerometer bias This choice was discussed in Example 49 on page 118

Assuming that the attitude is initialized by the method of Section 1031, then based on eqns (1014), (1015), and (1018) we can de ne a function atan2 (g2 , g3 ) 2 2 h(g, m) = atan2 g1 , g2 + g3 atan2( mw , mw ) 2 1 such that the initial values for the Euler angles are computed as g E = [ , , ] = h( , m) Using analysis similar to that described in Exercise 411 the covariance of the initial condition error vector [ E , xa ] is PE = Hg (Pa + Pf )Hg + Hm Pm Hm Pa Hg Hg Pa Pa

of a PNP transistor At B, the schematic symbol Electrodes are E = emitter, B = base, and C = collector

where Pa denotes the prior covariance of the accelerometer bias xa , Hg = h h g , Hm = m , and Pm is the covariance of the averaged magnetometer noise over the initialization period Also as described in Exercise 411, the covariance of the initial condition error vector [ , xa ] is PE = T Hg (Pa + Pf )Hg + Hm Pm Hm T Pa Hg T T Hg Pa Pa

where T is de ned in eqn (280) If we de ne P P a = = T Hg (Pa + Pf )Hg + Hm Pm Hm T T Hg Pa = Pa ,

Imagine a bipolar transistor as consisting of two diodes in reverse series You can t normally connect two diodes this way and get a working transistor, but the analogy is good for modeling the behavior of bipolar transistors A dual-diode NPN transistor model is shown in Fig 22-3A The base is formed by the connection of the two anodes The emitter is one of the cathodes, and the collector is the other cathode Figure 22-3B shows the equivalent real-world NPN transistor circuit

then the initial covariance matrix for the error state x is P 0 P a Pgg 0 P+ (t2 ) = P (t2 ) = 0 Paa Pa 0

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