Adaptive Constant On-Time Control
Adaptive Constant On-Time (ACOT) control is a variation where the on-time of the switch is adjusted based on input and output voltages to maintain a relatively constant switching frequency, combining benefits of both Constant On-Time (COT) and hysteretic controls. ACOT aims to provide the fast transient response of hysteretic control while stabilizing the switching frequency, which is beneficial for noise-sensitive applications.
In the block diagram of the TON generator, the current source ITON is proportional to VIN×K1, and VTH is proportional to Vo×K2. For the capacitor CTON, the current is equal to Cdvdt. Here, dv is equal to VTH, and dt is TON. Additionally, TON can be described via the basic transfer function of a buck converter. We can finally derive the equation for the period (TSW) which is independent of VIN and VOUT.
Figure 1
ACOT stability criteria involve ensuring that the system remains stable over a wide range of operating conditions. Stability in ACOT systems can be influenced by factors like the selection of hysteresis bands, the adaptive nature of the on-time, and the output filter's characteristics. Proper design considers phase and gain margins, potential for sub-harmonic oscillations, and how the system responds to load transients while maintaining a desired switching frequency. Stability analysis often involves Bode plots or time-domain simulations to ensure the system does not exhibit oscillations or diverge from its intended operation.
Here is an example of ACOT performance using the MIC2129 Pulse Width Modulation (PWM) controller. The graph on the left shows that the switching frequency deviation has been improved considerably with respect to input voltage, and the one on the right shows that the switching frequency deviation has been improved considerably with respect to output current.
Figure 2
DC Regulation Issue
Another problem is the DC regulation issue. We can solve this by adding a DC regulation enhancement block. This block includes an Operational Transconductance Amplifier (OTA) and compensation. The compensation consists of a low-pass filter and a unity gain buffer; in other words, it's an active low-pass filter. The OTA is an amplifier whose differential input voltage produces an output current. VCOMP is the output of the OTA and the input to the comparator. The OTA forwards the AC ripple from the feedback node to its output; it doesn't provide any AC gain and only provides DC gain. Therefore, for the feedback node, only a much smaller ripple is needed for precise control, which leads to an improved DC regulator.
Figure 3
ACOT Performance
Here is an example of ACOT performance, again using the MIC2129. The graph shows that the VOUT regulation has been improved considerably with respect to the input voltage.
Figure 4
Load Transient Response
One of the major advantages of COT controllers is their transient response. Because they don't have any clock, whenever a load transient occurs and the output voltage falls below the reference threshold, it immediately initiates the next pulse (assuming the minimum OFF time has expired, generally 200 ns). Therefore, the switching frequency is increased during the load transient. Next, consider the fixed frequency controller (for example, current mode control). When a load transient occurs, it needs to wait until the next switching cycle to correct it. So during the transient, the duty cycle is increased, the switching frequency remains constant, and the response delay can be as bad as Tclock. Figure 5 shows the best-case scenario where the load step occurs coincident with the clock.
Figure 5
ACOT Stability Criteria – Case 1
Large Output Voltage Ripple w/ High Equivalent Series Resistance (ESR)
Figure 6
Assuming the parasitic inductance of the output capacitor, or Equivalent Series Inductance (ESL), can be ignored, the total peak-to-peak output ripple voltage is the sum of a triangle wave created by the peak-to-peak ripple current in the inductor times the ESR of the output capacitor, and a sine wave caused by capacitor charging and discharging (with a 90-degree phase lag). For electrolytic capacitors, because their ESR is very high, the ESR ripple component dominates the total output ripple.
Abnormal Switching Behavior
ESR is Too Low
Figure 7
If the ESR of the output capacitors is low, abnormal switching behavior can occur. This may be because the ESR component of the ripple is of the same magnitude as the capacitive ripple component, resulting in the FB ripple being out of phase with the inductor current.
Critical ESR
Figure 8
To avoid this abnormal switching behavior, we can define a critical ESR (the minimum ESR to ensure stability with respect to this aspect).
ACOT Stability Criteria – Case 2
Medium Output Voltage Ripple
Figure 9
To achieve low input and output ripple and high performance, low ESR capacitors are used, such as tantalum or OS-CON (an aluminum solid capacitor with high conductive polymer). In this case, we recommend using a feed-forward capacitor between the output and the feedback node. This capacitor introduces a zero and a pole, providing a phase boost at mid and high frequencies. The DC gain remains unchanged at R2/(R1+R2), but the feed-forward capacitor provides additional high-frequency gain and phase boost.
ACOT Stability Criteria – Case 3
Very Low Output Voltage Ripple
Figure 10
Ceramic capacitors are used for low ripple and high performance. In this third case, we need to inject ripple from the switch node to the feedback node via an RC network. This network integrates the rectangular waveform from the switch node, converting it into a triangular waveform for the feedback node. A feedforward capacitor is also employed in this scenario. The equation for the VFB ripple using this method is shown in Figure 10.
Ripple Injection Circuit Details
Figure 11
For this case, there are two types of ripple injected into the feedback node:
- One comes from the switch node, which we call FB1. This is via Rinj and Cb. Here, VOUT acts as an AC ground.
- The other comes from the output via CFF, which we call FB2.
With appropriate design (covered later), we will achieve a stable system. We can visualize this with a vector diagram where the two vectors sum in phase with the inductor current:
VFB is in-phase with the inductor current, leading to a stable loop.
Derivation of Feedback Ripple Equation
Figure 12
Ripple Injection Stability Criteria
Figure 13
Additional stability criteria:
- CB is a DC blocking capacitor and must be of significantly larger magnitude than CFF.
- The impedance of CFF should be much less than R1 in parallel with R2.
- The time constant of R's * CFF should be much greater than the switching period. This is to ensure that the VFB ripple accurately represents the inductor current ripple.
Ripple Injection from PWM Controller
MIC2129 Example
Figure 14
For wide VIN applications, Microchip has developed an approach to inject ripple via a dedicated controller pin.
Analyzing ACOT Loop Gain with Ripple Injection
Figure 15
We can derive the overall loop gain for the system. First, we define various impedances in the circuit. Then, we outline the gains of the FB node and the LC filter (including the load). The overall loop gain can then be derived (without showing the complete derivation).
Figure 16
We recognize that the ratio of Z_B/Z_F plays an important role in enhancing the loop gain. From the basics of control theory, it is understood that the higher the loop gain, the closer the output approaches the command voltage (VREF). This results in improved accuracy of the actual output compared to the set value, enhancing both line and load regulation.