easa-part-66-module-4 Series Parallel

Diodes in Series and Parallel

4.1.1.8.1 Series Diode Configurations

For all the analysis to follow, it is assumed that

The forward resistance of the diode is usually so small compared to the other series elements of the network that it can be ignored.

This is a valid approximation for the vast majority of applications that employ diodes. Using this fact will result in the approximate equivalents for a silicon diode and an ideal diode that appear in Table 4.1. For the conduction region the only difference between the silicon diode and the ideal diode is the vertical shift in the characteristics, which is accounted for in the equivalent model by a dc supply of 0.7 V opposing the direction of forward current through the device. For voltages
less than 0.7 V for a silicon diode and 0 V for the ideal diode the resistance is so high compared to other elements of the network that its equivalent is the open circuit.

TABLE 4.1: Approximate and Ideal Semiconductor Diode Models.

For each configuration the state of each diode must first be determined. Which diodes are "on" and which are "off"? Once determined, the appropriate equivalent can be substituted and the remaining parameters of the network determined.

In general, a diode is in the "on" state if the current established by the applied sources is such that its direction matches that of the arrow in the diode symbol, and VD ≥ 0.7 V for silicon, VD ≥ 0.3 V for germanium, and VD ≥ 1.2 V for gallium arsenide.

Figure 4.1.1.26: Series diode configuration.

For each configuration, mentally replace the diodes with resistive elements and note the resulting current direction as established by the applied voltages ("pressure"). If the resulting direction is a "match" with the arrow in the diode symbol, conduction through the diode will occur and the
device is in the "on" state. The description above is, of course, contingent on the supply having a voltage greater than the "turn-on" voltage (VK) of each diode.

If a diode is in the "on" state, one can either place a 0.7-V drop across the element or redraw the network with the VK equivalent circuit as defined in Table 4.1. In time the preference will probably simply be to include the 0.7 V drop across each "on" diode and draw an open line through each diode in the "off" state.

The state of the diode is first determined by mentally replacing the diode with a resistive element as shown in Figure 4.1.1.27(a). The resulting direction of I is a match with the arrow in the diode symbol, and since E > VK, the diode is in the "on" state. The network is then redrawn as shown in Figure 4.1.1.27(b) with the appropriate equivalent model for the forward-biased silicon diode. Note for future reference that the polarity of VD is the same as would result if in fact the diode were a resistive element. The resulting voltage and current levels are the following:


VD = VK VR = E - VK ID = IR = VR/R (4)(5)(6)
Figure 4.1.1.27: (a) Determining the state of the diode of Figure 4.1.1.26; (b) substituting the equivalent model for the "on" diode of Figure 4.1.1.27a.

Figure 4.1.1.28: Reversing the diode of Figure 4.1.1.26

In Figure 4.1.1.28 the diode of Figure 4.1.1.26 has been reversed. Mentally replacing the diode with a resistive element as shown in will reveal that the resulting current direction does not match the arrow in the diode symbol. The diode is in the "off" state, resulting in the equivalent circuit of
Figure 4.1.1.28. Due to the open circuit, the diode current is 0 A and the voltage across the resistor R is the following:

VR = IRR = IDR = (0 A) R = 0 V

4.1.1.8.2 Parallel and Series-Parallel Configurations

The methods applied previously can be extended to the analysis of parallel and series-parallel configurations. For each area of application, simply match the sequential series of steps applied to series diode configurations.

Example: Determine V0, I1, ID1, ID2

Figure 4.1.1.29

Figure 4.1.1.30

For the applied voltage the 'pressure' of the source acts to establish a current through each diode in the same direction of the diode symbol. As the applied voltage is greater than 0.7 V, both

diodes are in the 'on' state, the voltage across parallel elements is always the same. V0= 0.7V

𝐼ଵ ൌ ௏ೃ ோ

ൌ

ாି௏ವ ோ

ൌ

ଵ଴௏ି.଻

.ଷଷ௞Ω = 28.18 mA

Assuming diodes of similar characteristics,

ID1 = ID2 = ூభ ଶ = ଶ଼.ଵ଼௠஺

ଶ

ൌ 14.09𝑚𝐴