Model of the DC-DC boost converter

In order to provide a sufficient voltage for a portable system from a micro-scale energy harvester, boost DC-DC pulse width modulated (PWM) converters are widely used. The boost converters can be classified into the asynchronous type and the synchronous type. A general diagram of an asynchronous boost converter is depicted in Figure 5.3. It consists of a power semiconductor switch Q, a diode D, an input filter inductor L, an output capacitor C, and a resistor R. A control signal, which has a switching cycle duration , is applied to the semiconductor switch Q to turn the converter on/off.

Figure ‎5.3 Simple asynchronous DC/DC boost converter structure

A synchronous boost converter circuit is shown in Figure 5.4. It has the same working principle as the asynchronous one. The difference between the two types of boost circuits is that a synchronous boost converter uses a p-type MOSFET with a proper control signal, depicted in Figure 5.4, to replace a diode D, as shown in Figure 5.3. Normally, a synchronous one is considered more efficient than an asynchronous one, because of avoiding using a big energy consuming diode in the circuit. Due to the high energy efficiency desired by the system, a synchronous type boost converter is selected as the power regulator circuit in this thesis.

Figure ‎5.4 Synchronous boost converter

Normally, a commercial boost converter is used to build a power conversion circuit for boosting a low input voltage to a constant high output voltage because of its high system efficiency, low cost and compact size. Hence, the boost converter should operate over a wide range of input voltages. However, the datasheets provided by the manufacturer, which only depict the energy efficiency curve of the circuit at a certain operation point. This is not sufficient for calculating the energy transfer efficiency of the boost converter, because the same device may be used at different input voltages.

Thus, in order to predict the performance of the boost converter in any input voltage conditions, a simulation model, which can provide a quick and easy way to obtain the system’s efficiency without needing to make laboratory measurements, is needed.

Over the last two decades various approaches to model DC-DC converters in continuous conduction mode (CCM) and discontinuous conduction mode (DCM) have been developed. Based on these existing works, an approach by identifying all of the individual power losses in the converter circuit as proposed in Aloisi and Palumbo (2005) and Liu et al. (2008) has been adopted in this chapter. The power losses in the inductor , the capacitor , the two MOSFET transistors and are the main power dissipation sources in a DC-DC converter circuit.

Despite many manufacturers stating that the power dissipation of the control circuit and the power lost in the miscellaneous circuit in the commercialized DC-DC converter IC are extremely low, these energy consumptions cannot be neglected in a micro energy harvesting system because of an ultra-low harvested energy. Similarly, the energy consumed by the MPPT control circuit, the static power dissipation of the

boost IC can be consumed independent of the load condition. Hence, the power consumed by the boost IC is expressed as:

_{， ，}

where _， , are the voltage across the boost IC and the quiescent current of the boost IC, respectively.

Then the power dissipation of the boost converter circuit can be expressed as adding these power dissipation sources together, as expressed in Equation 5.4.

(5.4) And the efficiency of the boost converter can be written as:

where is the power extracted from the energy generator, introduced in the previous section.

To achieve a simple numerical model, a generic model is adopted from Aloisi and Palumbo (2005). The advantage of using this model is that all the parasitic components and their power losses of the boost converter are considered. Figure 5.5 shows all the components of the boost converter in relation to their own parasitic resistance. In order to simplify the analysis, some assumptions, which are made by (Aloisi and Palumbo, 2005), have been used in this chapter.

 The N-type transistor Q is seen as a capacitor, parallel connection with a series combination of a linear resistor , and a switch , which can switch on or off by a control signal.

 Similar to N-type transistor Q, the P-type transistor is assumed as the capacitor connected with a series combination of a linear resistor and switch . is controlled by the boost IC.

 Passive components like inductors and capacitors are assumed to be linear, time invariant and frequency independent. In addition, the equivalent series resistance (ESR), and , of the inductor and the capacitor, respectively, are supposed to be independent from their operating temperature.

 Power dissipation in the control circuit is consumed at a constant value

in this work

 Assuming the transistor Q is turned on and off at the constant switching frequency, , where T is the entire switching cycle.

 R is the load resistor.

Figure ‎5.5 boost converter equivalent circuit including the parasitic components

As stated in the previous part, a boost converter can operate in DCM and CCM modes. These two modes are defined based on the inductor current condition of a boost converter circuit. The operation mode of DCM can be classified in terms of the energy stored in the inductor, which is delivered to the load during each switching cycle and the inductor current ramps down all the way to zero during the switch off time. Otherwise the mode is classified as CCM when only part of the energy is delivered to the load. As shown in many research works, the performance of a boost converter in the CCM and the DCM are significantly different in terms of voltage regulation and energy transfer efficiency. Thus, the model of a boost converter should be constructed in both of the CCM and the DCM, respectively.

(A) Boost converter in the CCM

Assume the boost converter is working in CCM. The ratio M, related to the input and output voltage can be obtained as follows:

where and are the output and input voltage of the boost converter and D is duty cycle of the boost converter, which is expressed as:

Equation 5.8 , the inductor current can be calculated by Equation 5.10.

(5.10)

(2) Power dissipation in N-type MOSFET

The power consumption of N-type MOSFET consists of a conduction loss , which is caused by the turn-on resistance , and a switching loss ,

which is caused by V-I overlapping and parasitic capacitances charge and discharge (Aloisi and Palumbo, 2005)

(5.11)

where is RMS current of switching the transistor. It is assumed that either the switching transistor current or voltage rises or falls linearly when the transistor switches. Then, the switching loss caused by parasitic capacitances and overlapping is ( ) (

) ( )

where and are the rise and fall times of drain-source voltage and drain current, respectively, and and represent the “on” state voltage of the MOSFET switch and the forward voltage drop in the body diode, respectively.

(3) Power dissipation in the P-type MOSFET

The power consumption of the P-type MOSFET ( ) is similar to the N-type MOSFET and it can be expressed as:

(5.14)

where is the on-time drain-to-source resistance of the P-MOSFET and is RMS current of the P-MOSFET.

(4) Power dissipation in the output capacitor

For the power dissipated by the output capacitor , it is caused by the ESR of the capacitor . The expression can be written as:

(5.15)

(5) Power dissipation in the entire boost converter circuit

The switching loss of the converter IC is neglected in the model in order to simplify the calculation. By collecting these power dissipation sources of the boost converter together, the total power dissipated by the circuit can be written as follows.

( )

(B) Boost converter in the DCM

When the boost converter is operating at the DCM, the formulae of the power dissipation of the inductor, the output capacitor and the N-type MOSFET switches are the same as expressed in the CCM. The differences are the expressions of and

(Aloisi and Palumbo, 2005).

( ) √

( )

By ignoring , the simulation model can be developed by integrating Equation 5.17 with Equation 5.16.

(C) Model Validation

A commercial synchronous boost converter TPS61222 (TPS61222, 2010) from TXAS instruments is employed in this chapter to evaluate the proposed model of the boost converter. This is because the TPS61222 has high system efficiency with an ultra-low input voltage, which can be operated as low as 0.7V input voltage range. The technical parameters are listed in Table 5.1 and all the parasitic parameters of the circuit components are extracted from their datasheets.

Table ‎5.1 Main technique parameters for TPS61222 and external components

Parameters Value

L, 4.7uH, 145mohms

C, 10uF, 2ohms

1000mΩ

600mΩ

2000kHz(2.4V)

TPS61222 Quiescent current

3.3V

Output voltage 5V

In order to identify the converter operating at the CCM or DCM, an approximation equation from the datasheet (TPS61222, 2010), has been used.

As long as the in-equation 5.19 is true, the boost converter operates in the CCM, otherwise the converter operates in the DCM. Then the model has been validated by comparing the efficiency curves, which are provided by the manufacturer in order to examine the accuracy of the model. A 5V constant output voltage has been set by the model. Then three types of input voltages (2.4V, 1.2V and 0.7V) have been simulated, respectively. The simulation results have been compared with the corresponding experimental results, supplied by the manufacturer, as shown in Figure 5.6. By examining the curves, the error of the model is around 5% in the worst case scenario.

Furthermore, in these three input voltage ranges, the converter circuit is most efficient when the 2.4V input voltage is applied and the 0.7V curve shows the circuit has the

lowest power conversion capability. This trend shows that when the input voltage is closer to the output voltage, the boost converter has a higher energy transfer capability.

Figure ‎5.6 Output current vs. Efficiency (2.4V and 1.2V input voltage)

Figure 5.7 shows the efficiency of the boost converter by the fixed output power in relation to the various input voltages. In order to show the difference, three output conditions (10mA, 1mA and 100uA) have been simulated. The simulation results have been compared with the corresponding efficiency curves described in the datasheet.

The error of the model is around 5% when comparing the results. In these three cases, the most efficient curve is found when the output current is fixed at 10mA. This is because the efficiency of the boost converter is increased with the increase of input power. In summary, the proposed model of the boost converter can be used to predict the energy condition of the regulator circuit.

Figure ‎5.7 Different input voltages vs. energy transfer efficiency