Kepco Power Solutions
718-461-7000
 by Liviu Pascu Each power supply, whether linear or switcher, uses at least two operating modes that characterize its operation: constant voltage (CV) and constant current (CC). The power supply can work in either one, while the other is usually a protective mode, both for the load and for the power supply itself. For example, a constant voltage supply will have a protective CC mode and a constant current supply will have a protective CV mode. The protective or limit mode can be designed to: Function as precisely as the main loop Be a rough limitation only Be designed to limit both output current and voltage, e.g., as in a power supply with a foldback-type limit feature, maintaining a quasi-constant dissipated power on the power control element. The transitions between these two modes, main operating mode and the protective mode, must be automatic and as smooth as possible. Unfortunately, that is not always the case because of the performance of the supply's error amplifier. However, this can be corrected by added a Forced Equilibrium Adapter that enables the error amplifier to cope with these operating mode changes.
To understand how the Forced Equilibrium Adapter works, we have to first look at the operation of a conventional power supply. Many variable power supplies have a rectangular voltage-current characteristic as shown in Figure 1(a). However, the rectangular characteristic is ideal, and can be applied only for small variations of the output voltage and current, especially near the "CR" point. In reality, the transfer characteristic and the transitions between the two modes, CV and CC, could be represented generically by Figure 1(b). During the transitions between modes, both the amplitude of the transients reached by output voltage and current, along with the duration of the transients, depend on:
• The particular structure of the error amplifiers used to control the power supply
• The difference between the new programming values and final output values
The characteristics illustrated in Figure 1(b) are undesirable because during these transitions the load receives uncontrolled energy which can possibly damage it.

### Figure 1. Rectangular type output characteristics for a unipolar power supply: (a) Ideal form, (b) Real - dynamic form

Eout, Iout = Actual values for output voltage and current;
Eprog, Iprog = Programming values for output voltage and current
CV, CC = Constant Voltage and Constant Current mode
CR = Critical mode  Figure 2 represents a common configuration used for linear type unipolar power supplies. A quick examination of the schematic reveals why the transitions between the two modes produce the transients depicted in Figure 1(b). The output voltage of the controlling error amplifier has a value of few volts, as determined by the configuration of the pass element and the value of the current sensing resistor (Rs), while the output voltage of the other error amplifier, which is out of control, is very close to the +Eaux rail. Each time control is switched between them, the output voltage of each error amplifier must swing from one value to the other. These swings are delayed by several factors,

### Figure 2. Functional schematic of a linear unipolar power supply with rectangular output characteristics.

PE = Pass Element (Power Element)
Ep = Primary DC Source
VEA, CEA = Voltage and Current Error Amplifiers
VR, CR = Voltage and Current Reference Circuits
VFC, CFC = Voltage and Current Feedback Circuits
EOR = Exclusive OR Circuit
Rs = Current Sensing Resistor
OF = Output Filter • The intrinsic delay of the operational amplifier working at its limit (close to +Eaux rail)
• The effective slew rate of the operational amplifiers used for both error amplifiers
• The time necessary to charge or to discharge the local feedback capacitors, C1 and C2, to the new output voltage of the corresponding error amplifiers.
Because the charge and discharge currents for these capacitors depend on the difference between the new programming value and the final output value, the perturbations introduced by C1 and C2 are "signal" dependent. Also, there is a delay introduced by the time required to charge or to discharge the overall voltage feedback capacitor C3 and the output filter capacitor C4. Due to these delays, during the transitions between modes, neither error amplifier is effectively in control, being at equilibrium. Thus, the output voltage and current take on uncontrolled values during this time.

The transients described above are significant for power supplies with a small value output capacitor, that produces a short equivalent time constant, compared with the other time constants in the supply. This kind of power supply could be a power amplifier or a regular power supply designed to work in two modes: "fast mode," with a small value output filter capacitor and "slow mode," with a large value output filter capacitor. When working in "slow mode" output transients are "absorbed" by the output filter capacitor, if it is big enough, which spares the load. However, the stress remains on the power supply, because, during transient, the current through the power element reaches an uncontrolled very high value when the output voltage of the power supply goes from a low to high value.

Figure 3 illustrates the error amplifier with Forced Equilibrium Adaptor, that significantly improves the power supply behavior by minimizing transients appearing at the output when the control of the power supply changes from one error amplifier to the other.

The circuit functions as follows: when the error amplifier is in control, IC1 - the Basic Error Amplifier (BEA) regulates the potential at the pass element (PE) input and eventually the output signal (voltage or current). Current through R11 is sunk partially, depending of the structure of the pass element, by IC1. The voltage drop on R5, VR5 >> VOS (VOS = offset input voltage of IC101), is positive with respect to the input of IC101 of the Forced Equilibrium Adaptor (FEA) It is sufficient to force its output to the positive rail of the auxiliary supply (+Eaux). At this time diode D101 is off, so the Forced Equilibrium Adaptor will not affect the equilibrium at the input of the error amplifier when the main loop is closed: Va = 0V and then, Vfbk / R1 = Vprog / R2.

Thus with D101 off, the Forced Equilibrium Adaptor will not interfere with the normal operation of the regulating loop, performed by the controlling error amplifier. The solid line above R5 in Figure 3 represents the current flowing through R5 in this situation.

Because the other error amplifier has a similar structure, we can apply similar reasoning while referring to Figure 3 and the schematic of a generic power supply shown in Figure 2. In this case, because Vfbk / R1 < Vprog / R2, the potential Va will be positive, forcing the output of IC1 toward the positive rail of the auxiliary supply. However, then the current through R5 sourced by IC1 through R5 and R104 toward -Eaux, (broken line below R5 in Figure 3), tries to change direction, IC101, upon receiving a negative input, it changes the polarity of its output from positive to negative, thus forward biasing diode D101. With diode D101 ON, IC101 will close a local loop around the basic error amplifier IC1 due to the huge open-loop amplification factor, keeping VR5 = VOS.

### Figure 3. Schematic of the Error Amplifier with Forced Equilibrium Adaptor.

PE = Pass Element (Power Element)
BEA = Basic Error Amplifier
EOR = Exclusive OR Circuit
-Vfbk = Feedback Signal
+Vprog = Programming (reference) Signal
+Eaux, -Eaux = Auxiliary internal power supplies
Va = Equilibrium node voltage
Vf = Forcing equilibrium voltage At this time the adaptor circuit forces equilibrium, from the point of view of the overall loop, at the input of the error amplifier. So again, Va = 0V, but now Vf / R103 + Vfbk / R1 = Vprog / R2.

The values of R104 and R5 are chosen such that Eaux / R104 > VOS / R5.

So, even if the error amplifier does not control the overall loop through its corresponding diode (D1 or D2), a small current will flow through D1 or D2, from +Eaux through R11 toward -Eaux The result is the diode is forward biased so that it is ready to work when the error amplifier takes control. Furthermore, the voltage drops across the local feedback capacitors C1 and C2 in Figure 2, placed around the error amplifiers, are almost equal; the difference is merely 0.1 to 0.2V, given by the difference between the voltage drop across the diodes D1 and D2, where the "controlling" diode conducts more current than the "non-controlling" diode. This is very important, because it minimizes the time required to update the charges across the feedback capacitors when the control is switched between error amplifiers.

To obtain maximum performance from the circuit, IC101 should be a high slew rate type op amp, with very small bias currents. The amplifier IC1 can remain the one initially chosen for the application. Generally, it must be an op amp with very small bias currents, input offset voltage and input offset current. No special restrictions are imposed on the slew rate. Zener diode D102 limits the excursion at the output of the error amplifier upon power-on of the circuit and when the output is programmed from a high value to a low value.

Figures 4 and 5 compare the output current and voltage from a power supply of 2000VDC / 0.1ADC (adjustable from zero to the nominal values), working in "fast mode," when the power supply is driven from CV to CC mode. The waveforms are recorded for the power supply using regular error amplifiers (Figures 4(a) and 5(a)) and using Error Amplifiers with Forced Equilibrium Adaptor (Figures 4b and 5b).

### Figure 4. Output current (CH1 = 20mA/cm) and output voltage (CH2 = 50V/cm) for a power supply driven from CV to CC. (a) Regular error amplifiers, (b) Error amplifiers with forced equilibrium adaptors.

Initial programming: Eprog = 0Vdc, Iprog = 20mADC;
Initial status: Eout = 0Vdc, Iout = 0mADC, Voltage mode
Final programming: Eprog = 133Vdc, Iprog = 20mAdc
Final status: Eout = 108Vdc, Iout = 20mAdc, Current mode  Observing the waveforms from Figures 4(a) and 5(a), it can be seen that, for regular error amplifiers, the transient at the output could be big - almost two times bigger than the programmed output (see Figure 5a)It is strongly dependent (amplitude and duration) on the difference between the new programming value and the final output value. The waveforms from Figures 4(b) and 5(b) show that the transients are completely removed by the error amplifiers with the Forced Equilibrium Adaptor.

From the above description, the advantages of the error amplifier with Forced Equilibrium Adaptor could be summarized as:

• Reduces the overall output transition time and implicitly minimize output transition amplitude during time that the error amplifier either is going out of control or is coming under control. This is accomplished by making the swing at the output of the error amplifiers almost zero and keeping the "non-controlling" error amplifier and the corresponding OR diode in a ready state.
• Allows a much smaller local feedback capacitor to be used to make the loop stable, thereby again reducing the transition time and amplitude at the overall output
• The circuit is very simple and can easily be adapted to the existing error amplifiers
• The circuit can also be applied to other kind of instruments, devices or installations configured to use two or more error amplifiers "fighting" to control the same process.

### Figure 5. Output current (CH1 = 20mA/cm) and output voltage (CH2 = 50V/cm) for a power supply driven from CV to CC: (a) Regular error amplifiers, (b) Error amplifiers with forced equilibrium adaptors.     