{"id":385277,"date":"2024-06-29T06:01:14","date_gmt":"2024-06-29T06:01:14","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=385277"},"modified":"-0001-11-30T00:00:00","modified_gmt":"2024-06-29T06:01:14","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=385277","title":{"rendered":"SEPIC-\u0106uk split-rail converter average model<\/span>"},"content":{"rendered":"
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SEPIC-\u0106uk split-rail converter can be used to make positive and negative supplies from a single input voltage for relatively well-matched loads like operational amplifiers.<\/p>\n

Transient models are time consuming. Average models reduce modeling time drastically.<\/p>\n

The PWM switch average models for current- and voltage-mode are described in details in Christophe Basso\u2019s book \u201cSwitch-Mode Power Supplies, Second Edition: SPICE Simulations and Practical Designs\u201d. Using of these models for SEPIC and \u0106uk converters is also shown.<\/p>\n

This text shows how to use the PWM switch average model to design a split-rail SEPIC-\u0106uk converter.<\/p>\n

Circuit<\/h2>\n

The SEPIC-\u0106uk split-rail converter is described in [5] and can be used with uncoupled and coupled inductors.<\/p>\n

\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail converter circuits<\/figcaption><\/figure>\n

This circuit uses 3 switches, the power switch SW1 and 2 diodes, SD1 and SD2. It creates difficulties in using of the PWM switch average model which is a toggle switch with 2 positions.<\/p>\n

Circuit transformation<\/h2>\n

The transformation steps are shown in the picture below.<\/p>\n

\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail converter transformation steps<\/figcaption><\/figure>\n

The ideal diode D1 is added to split the current paths and to use only one toggle switch.<\/p>\n

Unfortunately, there is no common wire between the output voltages now.<\/p>\n

SEPIC-\u0106uk split-rail converter with uncoupled inductors<\/h2>\n

The average model of the converter with 4 V input and +\/\u221212 V 0.5 A outputs is shown in the picture below.<\/p>\n

\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail converter average model, TINA-TI<\/figcaption><\/figure>\n

The U2 differential amplifier and the Vref voltage source are used to make the DC operating point. The voltage-to-voltage converter E1 is used to make the connection with the feedback circuit either with the positive or negative output.<\/p>\n

TINA-TI does not have a model for the ideal diode, this macro was used:<\/p>\n

.subckt d_ideal a k d1 a k dio .model dio d is=1e-15 n=1m .ends d_ideal<\/code><\/pre>\n
A simple transient model was used to verify the average model. The same circuit was run in LTspice with SPICE engine and SIMPLIS with piecewise linear (PWL) modeling.<\/p>\n
\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail CM CCM transient model, LTspice<\/figcaption><\/figure>\n
The small-signal control-to-output transfer functions for this SEPIC-\u0106uk split-rail converter with uncoupled inductors are shown in the pictures below.<\/p>\n
\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail converter small-signal control-to-output transfer function, the average model, TINA-TI<\/figcaption><\/figure>\n
\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail converter small-signal control-to-output transfer function, SIMPLIS<\/figcaption><\/figure>\n
\"SEPIC-\u0106uk
SEPIC-\u0106uk split-rail converter small-signal control-to-output transfer function, LTspice<\/figcaption><\/figure>\n
There are the visible differences:<\/p>\n