The Voltage Divider

The output Vo of the power supply first goes to a voltage divider. Here it is in effect, just stepped-down, for subsequent comparison with the reference voltage Vref- The comparison takes place at the input of the error-amplifier, which is usually just a conventional op-amp (voltage amplifier). 

So this tells us what ratio of the voltage divider resistors we must have, to produce the desired output rail. 

Note The lower resistor of the divider, Rfl, does not enter the ac analysis, provided we are considering ideal op-amps. In practice, it does affect the bandwidth of a real op-amp, and therefore may on occasion need to be considered. 

Note If we are using a spreadsheet, we will find that changing Rfl does in fact affect the overall loop (even when using conventional op-amp-based error amplifiers). But we should be clear that that is only because by changing Rfl, we have changed the duty cycle of the converter (its output voltage), which thus affects the plant transfer function. Therefore, in that sense, the effect of Rfl is only indirect. We will see that Rfl does not actually enter into any of the equations that tell us the locations of the poles and zeros of the system. 

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First select a voltage divider sense current—a nominal 1mA. Determine the lower resistor (RIO + Rll) in the voltage divider ... 

Then find the value of the feedback capacitor C. The designer knows the value of the input resistor (R). It is the upper resistor in the voltage divider responsible for the voltage feedback to the error amplifier. One then performs Equation B.15. 

We built up two HV rectifier banks. Each was good for over 40,000 volts. The diodes we used are 1000 Volt, 1 Amp. We used 48 in one diode bank and 58 in the other. We put a 1 meg ohm resistor across each diode to make sure that the voltage divides equally. 

HI1HLYTIC SDLUTIQn At low frequencies, the capacitor is an open circuit and the voltage at VOUt can be obtained by the voltage divider of R3 and R4 ... 

An expression for the gain can now be obtained from the voltage divider of R4 and Z ... 

Thus, we should expect the magnitude plot to start at a negative value in decibels and finish at -6 dB. The next question is, where are the poles and zeros The gain of the circuit can be obtained from the voltage divider of R f, R2, and Cl ... 

We will now change the voltage divider circuit to use the resistor model RSpCilt. To change the model reference of a resistor, double-click the LEFT mouse button on the text RSguuSS ... 

We will run a Monte Carlo analysis on the voltage divider circuit previously described. The circuit and parts are repeated below ... 

EXERCISE 9-2 What percentage of the voltage divider circuits will have a gain of 0.49 or greater if 10% resistors with a Gaussian distribution are used ... 

The Performance Analysis can be used in conjunction with the Monte Carlo analysis to view the distribution of a parameter as a function of device tolerances. For this example, we will display how the spread of the gain V(Vo)/V(Vl) varies with resistor tolerances. We will use the voltage divider of the previous section and 5% resistors with a uniform distribution ... 

We can draw a few conclusions about using the Monte Carlo and Worst Case analyses from the results of the voltage divider circuit. 

V0/V/ (fti), to the analytical expression with recovery of the complete quartz impedance near resonance (admittance, conductance and impedance). Although the voltage divider method does not measure the transfer function phase and hence it is not possible to demonstrate the validity of BVD circuit, it has the advantage of speed. Also passive methods like TFM can be applied under high viscous damping so that the shear wave phase never crosses zero and the EQCM no longer resonates. 

Fig. 12.5. Flowchart describing the voltage divider transfer function method (TFM) Real time measurement and nonlinear fit to the BVD equivalent electrical circuit.

Figure 17 Configuration of op amp to function as a potentiostat. The desired Vin is set by the experimenter via the voltage divider on the left, which consists of a battery and a variable resistor. The path of the current is shown, indicating that no current passes through the RE.

Fig. 4. Schematic of conductometric detection, (a) The voltage divider string, (b) The bridge configuration.

For the voltage divider string arrangement of Fig. 4(a), the signal voltage is written as... 

The current that the pressure switch turns on or off is provided by the voltage divider, current reducing circuit in the controller which consists of three resistors. 

The feedback block, on the other hand, consists of the voltage divider (if present) and the compensated error amplifier. Note that we may prefer to visualize the error amplifier block as two cascaded stages — one that just computes the error (summation node), and another that accounts for the gain (and its associated compensation network). Note that the basic principle behind the pulse width modulator stage (which determines the shape of the pulses driving the switch), is explained in the next section, and in Figure 7-11. 

Let us now lump the entire feedback section, including the voltage divider, error amplifier, and the compensation network. However, depending on the type of error amplifier used, this must be evaluated rather differently. In Figure 7-13 we have shown two possible error amplifiers often used in power converters. 

Note that the reference designators of the components have changed in this section for convenience. What we are now calling Rl was Rf2 when we previously discussed the voltage divider. Similarly, the gray unnamed resistor in Figure 7-15 was previously called Rfl. ... 

Note The way we have separated the terms of the transconductance op-amp, the pole-at-zero (fpO H3) seems to be dependent only on Cl (no resistance term). However, we could have also clubbed the voltage divider section HI along with H3 (since these are simply cascaded blocks, in no particular order). Then the pole-at-zero would have appeared differently (and also included a resistance term). However, whichever way we proceed, the final result, that is, H, will remain unchanged. In other words, HI, H2, and H3 are just intermediate mathematical constructs in calculating H (with no obvious physical meaning of their own necessarily). That is why the actual pole-at-zero frequency of the entire feedback block is designated as fpO, not fpO H3. 

We choose our target crossover frequency fcross as 50 kHz. We pick Rf2 = 4 kf2 and Rfl = 1 kf2 based on the voltage divider equation, the output voltage, and the reference voltage. Then... 

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