Unified LTspice AC Model for Current Mode DC-DC Converters

[Introduction]When power supply designers want to get an overview of the feedback loop of a power supply, they use loop gain and phase Bode plots. Knowing that the loop response is predictable can help narrow the selection of feedback loop compensation components.

Introduction

When power supply designers want to get an overview of a power supply’s feedback loop, they use loop gain and phase Bode plots. Knowing that the loop response is predictable can help narrow the selection of feedback loop compensation components. An accurate way to generate gain and phase diagrams is to connect power on the test bench and use a network analyzer; however, in the early stages of design, most designers choose to use computer simulations to quickly determine the approximate range of component selection, Also, get a more intuitive understanding of the loop’s response to parameter changes.

This paper mainly studies the feedback control model suitable for the current mode control power supply. Current-mode control is fairly common in switch-mode DC-DC converters and controllers, and offers several advantages over voltage-mode control: better line noise rejection, automatic overcurrent protection, easier parallel operation, and Improved dynamic response.

Designers already have access to a number of current-mode power supply averaging models. Some models are accurate to half the switching frequency and can match increasing converter bandwidths, but are only suitable for limited topologies such as buck, boost, and buck-boost (not 4-switch buck-boost). pressure). Unfortunately, 3-port or 4-port averaging models for topologies such as SEPIC and Ćuk are not yet half as accurate as the switching frequency.

This article presents LTspice® simulation models that are accurate to half the switching frequency (even at relatively high frequencies) and are suitable for a variety of topologies, including:

Buck

boost

Buck-Boost

SEPIC

Ćuk

Forward

Flyback

This paper presents a piecewise linear system (SIMPLIS) simulation of results to determine the validity of the new model and exemplifies specific applications of the model. In some examples, the test results are used to validate the model.

Current Mode Control Models: A Brief Overview

In this section, we will reiterate some important points about the current mode control model. For a more complete understanding of current mode models, please refer to the publications mentioned in the “References” section at the end of this article.

The purpose of the current loop is to make the Inductor current follow the path of the control signal. In the current loop, the average inductor current information is fed back to the modulator with detection gain. The modulator gain, Fm, can be calculated geometrically, assuming that the constant inductor current is ramped up, and the external compensation current is also ramped up. To simulate the effect of a ramp-up change in the inductor current, we add two additional gains to the model: a feedforward gain (kf) and a feedback gain (kr), as shown in Figure 1.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 1. Average model for current mode control, drawing: RD Middlebrook

To extend the validity of the averaging model shown in Figure 1 to the high frequency range, the researchers propose several improved averaging models based on the results of discrete-time analysis and sample data analysis. In RB Ridley’s model (see Figure 2), the sample-and-hold effect can be equivalently represented by the He(s) function, which can be inserted into the inductor current feedback path of the continuous average model. Since the model is evolved from a discrete-time model, subharmonic oscillations can be accurately predicted.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 2. Averaged model for improved current mode control, drawing: RB Ridley

Another improved average model was proposed by FD Tan and RD Middlebrook. To account for sampling effects in the current loop, one more pole must be added to the current loop gain derived from the low frequency model, as shown in Figure 3.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 3. Averaged model for improved current mode control, plot: FD Tan

In addition to RB Ridley’s model, the current control model proposed by RW Erickson is also very popular. The inductor current waveform is shown in Figure 4.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 4. Steady State Inductor Current Waveform with External Compensation Ramp Up

The average inductor current is expressed as:

Unified LTspice AC Model for Current Mode DC-DC Converters

where iL is the detected current, ic is the current command issued by the error amplifier, Ma is the applied compensation ramp, and m1 and m2 are the rising and falling ramps of the output inductor current, respectively. Perturbation and linearization results:

Unified LTspice AC Model for Current Mode DC-DC Converters

From this formula and the canonical switching model, a current mode converter model can be derived.

A new and improved averaging model

RW Erickson’s model can help power-supply designers gain insight from a physical perspective, but it’s less than half as accurate as the switching frequency. To extend the validity of this model to the high frequency range, we propose a modified averaging model based on the results of discrete-time analysis and sample data analysis (see Figure 5).

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 5. The proposed improved current mode control averaging model

According to the inductor dynamic sampling data model, it can be concluded that:

Unified LTspice AC Model for Current Mode DC-DC Converters

where T is the switching period,

Unified LTspice AC Model for Current Mode DC-DC Converters

The Gic(s) of the model shown in Figure 5 can be derived:

Unified LTspice AC Model for Current Mode DC-DC Converters

where ωc is the crossover frequency of the inner current loop Ti, as shown in Figure 5, see Table 1 for the value of ωc for various topologies.

Table 1. Internal Current Loop Crossover Frequency (ωc) for Different Topologies

Unified LTspice AC Model for Current Mode DC-DC Converters

*For two separate inductors, L=L1×L2/(L1+L2)

**NSP is the secondary to primary turns ratio

Buck Converter Example

In Figure 5, we connect the Fv feedback loop in parallel with the iL feedback loop. We can also consider the Fv feedback loop as the inner loop of the iL feedback loop. Figure 6 shows the complete buck converter model with additional Gic(s) stages.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 6. Block Diagram of Improved Buck Converter Averaging Model

The control-to-output transfer function Gvc(s) is

Unified LTspice AC Model for Current Mode DC-DC Converters

The current loop gain Ti (s) and the voltage loop gain Tv (s) can be calculated by the following equations:

Unified LTspice AC Model for Current Mode DC-DC Converters

and

Unified LTspice AC Model for Current Mode DC-DC Converters

in:

Unified LTspice AC Model for Current Mode DC-DC Converters

In Figure 7, the calculated loop gain based on the new current mode model agrees with the SIMPLIS result. In this example, VIN = 12 V, VOUT = 6 V, IOUT = 3 A, L = 10 µH, COUT = 100 µF, fSW = 500 kHz.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 7. MathCAD results compared to SIMPLIS results (fSW = 500 kHz)

4-port model with LTspice

A 4-port model is constructed based on the modified averaging model shown in Figure 5. In closed-loop operation, this 4-port model can be used to analyze PWM topologies using standard circuit analysis programs such as the free LTspice to determine DC and small-signal characteristics.

Figure 8 shows a simulation schematic of a simulation of various topologies using LTspice, using the same model for each topology. The feedback resistor divider, error amplifier, and compensation components are not shown. To use this model for a real DC-DC converter model, connect the output of the error amplifier to the VC pin.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 8. Using the LTspice model to simulate various topologies: (a) Buck, (b) Boost, (c) SEPIC, (d) Ćuk and (e) Flyback.

See Table 2 for the various LTspice behavioral voltage source commands shown in Figure 8. E1 represents the voltage applied to the inductor when the switch is on, E2 represents the voltage applied to the inductor when the switch is off, V3 represents the slope compensation amplitude, and Ei represents the inductor current.

Table 2. LTspice Behavior Voltage Source Commands for the Circuit Shown in Figure 8

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 9 shows the simulation results for a SEPIC converter with 2 independent inductors, which match the SIMPLIS results at half the switching frequency. In this example: VIN = 20 V, VOUT = 12 V, IOUT = 3 A, L = 4.7 µH, COUT = 120 µF, C1 = 10 µF, fSW = 300 kHz.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 9. Comparison of LTspice and SIMPLIS simulation results for SEPIC converter (fSW = 300 kHz)

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 10. LT3580 LTspice Model

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 11. Bode Plot (fSW = 2 MHz)

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 12. 4-Quadrant Controller LTspice Model Using LT8714

Test validation of new models

The new LTspice model shown in Figure 11 is tested and validated for topologies not supported by previous legacy models, including Ćuk, 4-quadrant, and 4-switch buck-boost topologies.

Validation of the Ćuk controller model on the test bench

The LT3580 is a PWM DC-DC converter with an internal 2 A, 42 V switch. The LT3580 can be configured as a boost, SEPIC or Ćuk converter, and its AC model is suitable for all of these topologies. Figure 10 shows a Ćuk converter where fSW = 2 MHz and VOUT = –5 V. Figure 11 compares the LTspice simulated Bode plot and actual test results, which are in good agreement over half the switching frequency range.

Validating the 4-quadrant controller model on the test bench

The LT8714 is a synchronous PWM DC-DC controller designed for 4-quadrant output converters. The output voltage transitions through 0V undisturbed by sinking and sinking output functions. When configured for the new 4-quadrant topology, the LT8714 is ideal for regulating positive, negative or 0V outputs. Applications include: 4-quadrant power supplies, high power bidirectional current sources, active loads, and high power, low frequency signal amplification.

The output voltage may be positive or negative based on the CONTROL pin voltage. In the example shown in Figure 12, when the pin voltage is 0.1 V, the output voltage is –5 V, when the pin voltage is 1 V, the output voltage is 5 V, VIN is 12 V, and the switching frequency is 200 kHz .

Figure 13 compares the Bode plots simulated by LTspice with the plots obtained from actual testing—their results are very consistent at half the switching frequency. The control voltage (CONTROL) is 1 V, which makes VOUT (OUT) 5 V.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 13. Bode Plot (fSW = 200 kHz)

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 14. Bode Plot (fSW = 200 kHz)

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 15. LT8390 LTspice Model

Figure 14 compares the Bode plots simulated by LTspice and the actual test results—their results are very consistent at half the switching frequency. The control voltage (CONTROL) is 0.1 V, which makes VOUT (OUT) -5 V.

Verification of 4-Switch Buck-Boost Model on Test Bench

The LT8390 is a synchronous 4-switch buck-boost DC-DC controller that regulates the output voltage (and input or output current) based on input voltages above, below or equal to the output voltage. A proprietary peak-buck/peak-boost current mode control scheme supports adjustable fixed frequency operation.

The LT8390 LTspice AC model automatically selects one of four operating modes by monitoring the input and output voltages: buck, peak-buck, peak-boost, and boost. Figure 15 shows an example circuit for the LT8390. Figure 16 and Figure 17 show the LTspice simulation results and actual test results for the buck and boost modes, respectively. Over half the switching frequency, the two curves agree very well.

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 16. Bode plot (fSW = 150 kHz). VIN = 20 V, VOUT = 12 V, IOUT = 5 A

Unified LTspice AC Model for Current Mode DC-DC Converters

Figure 17. Bode plot (fSW = 150 kHz). VIN = 8 V, VOUT = 12 V, IOUT = 5 A

Summarize

By building this current-mode control model, it provides both the accuracy of the sample data model and the simplicity and versatility of the 4-port switch model. This article presents a unified LTspice model that remains accurate at half the switching frequency for buck, boost, buck-boost, SEPIC, Ćuk, flyback, and forward topologies. Compare LTspice simulation results with actual test results for verification. This model is suitable for analyzing loops when designing current mode converters in continuous conduction mode.

(Source: Analog Devices, Author: Wei Gu, Application Director of Power Products)


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