The constant on-time (COT) regulator is a modified version of thetypical hysteretic converter. A typical hysteretic converter turns onthe main switch for a fixed interval of time whenever the outputvoltage drops across the reference voltage, while the t off is modulatedfor regulating the output voltage “valley.”
By programming the fixed t on to be an inverse function of theinput voltage, the operating frequency of the regulator is nearlyconstant at continuous-conduction mode.
A COT regulator (Figure 1, below )iswidely used, as it provides fast transient response and does notrequire tedious loop compensation.
|Figure1: (top) A COT regulator is widely used, as it provides fast transientresponse and does not require tedious loop compensation; (bottom) Theequation for predicting the minimum ESR for achieving stability isverified by a conventional COT buck regulator.|
But the main constraint of a conventional COT regulator is itsrequirement for tens to hundreds milli-ohm of output capacitor's equivalent series resistance (ESR)to provide stable voltage output.
Thus, a low-profile ceramic capacitor with low ESR value (<10milli-ohms) is not favorable. Empirically, a larger-than-enough ESRvalue is selected by experiments, as there is no rule of thumb inestimating the minimum required ESR. Although a large ESR canensure stability, it enlarges output ripple, and hurts outputregulation and power efficiency.
For a COT regulator, t on is fixed. The t off is modulated for output voltage regulation by the negativefeedback mechanism. The feedback comparator signals when to end thetoff and trigger a new switching cycle.
This happens during the t off when V o < V ref , where V o = V ref + V c + V ESR ;V c is the output capacitorvoltage component; and vESR isthe voltage across the ESR perturbed by the triangular waveform of theinductor current.
After normalization with respect toV ref , a new switching cycle is triggeredwhen V c + V ESR < 0 or V c < -V ESR . There are two different operatingmodes for two different ranges of ESR. If ESR is too small, thereexists an operating mode such that sub-harmonic oscillation occurs, as V c < -V ESR is fulfilled before fixed t on has elapsed.
In this case, a new switching cycle is triggered prematurely.Although output voltage can still be regulated, t off is not modulatedin a cycle-by-cycle manner with respect to the switching frequency, butwith its sub-harmonic.For large enough ESR,
within the switching period, sub-harmonicoscillation is not possible, and the regulator is guaranteedstable.
|Figure2: ESRc is the minimum ESR, making instantaneous slope of -VESR morenegative than that of Vc at the moment right after toff ends.|
There is a critical ESR value (ESR c ), where the ESR value is just largeenough to stabilize the COT regulator (Figure2, above ). Although the regulator remains stable with increasingESR, the output ripple voltage increases simultaneously. ESRc is theminimum ESR, making instantaneous slope of -V ESR more negative than that of V c at the moment right after t off ends.
From the equation, the criterion for stability is
With an ESR larger than ESRc, the regulator is still stable, butwith a larger output voltage ripple due to the increase of VESR.
The critical ESR formula gives a good estimation of the outputcapacitor's minimum ESR value, ensuring stability while keeping theoutput ripple as small as possible for the COT buck regulator.
The equation above for predicting the minimum ESR for achievingstability is verifiedby a conventional COT buck regulator (Figure1b earlier ).
|Figure3: The measurement results match with the proposed criterion forstability.|
Figure 3 above shows theminimum ESR required to prevent the occurrence of subharmonicoscillation with step load of 200mA for given t on and C out . The measurement results matchwith the proposed criterion for stability.
|Figure4: Because only the toff is being modulated, the negative ramp portionof VESR contains the necessary attributes for stability.|
Flywheel current injection control
For a COT buck regulator, t on isfixed. Only the t off is modulated with respect to theloading condition. Being a triangular waveform, V ESR consists of two portions – one is formed by the positive ramp duringthe t on and the other is formed by thenegative ramp during t off (Figure4, above ). Because only the t off is being modulated, the negativeramp portion of V ESR containsthe necessary attributes for stability.
Flywheel current injection control (FCIC) was invented (patentpending) based on such a presumption. The working principle isillustrated in Figure 2 earlier. During t off , the re-circulating inductorcurrent (flywheel current) flows from ground through the sync-switchand the inductor to the output (Figure5, below ).
|Figure5: (a) The COT buck regulator accepts an input voltage range as wide as4.5-36V; (b) The COT buck regulator with FCIC can achieve a maximumefficiency of 93 percent.|
If we have R j asthe sensing resistance, the inverted V sen is just the replication of theportion of V ESR during t off . By adding V sen to the DC reference voltage and comparing the resultant voltagewith V o , the function of ESR for stabilitycan be substituted by that of R j . No external ESR is required forthe output capacitor.
R j can be a well-controlled on-chipresistor or simply be the resistance of the sync-switch that isnominally larger than the required critical ESR. Then, stability isguaranteed without ESR. Hence, a low-profile ceramic output capacitorcan be used, while output voltage ripple can be kept very low.
|Figure6. With the use of a ceramic output capacitor, output ripple voltage isless than 5mV.|
The block and application diagrams of a COT buck regulator with FCICare shown in Figure 3 earlier .It accepts an input voltage range as wide as 4.5-36V and can achieve amaximum efficiency of 93 percent. A ceramic output capacitor is used sothat output ripple voltage is less than 5mV . Its load transient response isshown in Figure 6 above, whereV in = 18V, V out = 3.3V, C out = 2 * 47 microfards and f sw =1MHz.
Further applying FCIC with the critical ESR makes the COT buckregulator simpler. FCIC removes the ESR constraint to ensure thestability of a COT regulator, allows the use of a ceramic outputcapacitor and minimizes the output ripple voltage.
Lawrence H.S. Ling is PrincipalDesign Engineer, and Issac Hsu and Gladis Koon are Circuit DesignEngineers at National Semiconductor.To read a PDF version of this article, go to “ImproveCOT regulator performance with FCIC.”