EE464-Static Power Conversion-II

class: center, middle

# EE-464 STATIC POWER CONVERSION-II

# Resonant Converters

## Ozan Keysan

## [keysan.me](http://keysan.me)

### Office: C-113 <span class="meta">•</span> Tel: 210 7586

---

## Advantages of High Switching Frequency?
--

- ### Reduces filter element sizes
--

- ### Reduces transformer size
--

- ### Reduced ripple

## Disadvantages of High Switching Frequency?
--

- ### Increased switching losses

---

# Switching Loss

### You have more turn-on, turn-off energy dissipation as the frequency increases
---

# Hard Switching vs. Soft Switching
--

---

# Hard Switching vs. Soft Switching
--

---
# Resonant Converters
--

## Two main types of switching:
--

- ## when voltage is zero (ZVS)
--

- ## when current is zero (ZCS)

---
 
# Resonant Converters
--

### There are many resonant converter topologies.

### Most common types:
--

- ## Resonant Switch Converters
--

- ## Load Resonant Converter
--

- ## Resonant DC-link Converter
---

# Review: RLC Resonant Circuits
--

---

# Review: RLC Resonant Circuits

---

# Review: RLC Resonant Circuits

- ### [Series RLC Circuit Animation](http://mathlets.org/mathlets/series-rlc-circuit/)

- ### [Series RLC Circuit Animation](https://www.edumedia-sciences.com/en/media/545-rlc-series-circuit)

- ### [Signal Transmission and Reflection](https://www.youtube.com/watch?v=ozeYaikI11g)

---
# Resonant Switch Converter: Zero Current Switching

#### W. Hart., Power Electronics, Ch.9
--

#### Assumption: \\(L_o\\) is large enough, \\(I_o\\) is constant
---

## Operating Mode: \\(t < 0\\)
--

### Switch open, Diode ON (frewheeling), \\(v_C = 0\\)

---

## Operating Mode: \\( 0 < t < t\_1\\)
--

### Switch closed, \\(L_r\\) start charging

### \\(i_{L} < I_o \\) so the diode is still ON

---

## Operating Mode: \\( t\_1 < t < t\_2\\)
--

### When \\(i_{L} = I_o \\), the diode turns OFF

### Excess inductor current charges the capacitor  \\(v_C > 0\\)

---

## Operating Mode: \\( t\_1 < t < t\_2\\)
--

## If no action is taken, oscillation starts in the  LC circuit!

---

## Operating Mode: \\( t\_2 < t < t\_3\\)
--

## Turn the switch off, when \\(i_{L} =0 \\)
--

## =Zero current switching!
--

## Alternatively a unidirectional switch (SCR) can be used.

---

## Operating Mode: \\( t\_2 < t < t\_3\\)
--

### Very small switching loss (due to capacitances in the switch)

### Output current is supplied by C (discharges linearly)

---

## Initial Mode:  \\( t\_3 < t < T\\)
--

###  \\(v_C = 0\\), diode starts freewheeling,
### Switch ready to to turn ON (zero current)

---

## Analysis of the Operating Modes

#### W. Hart., Power Electronics, Ch.9-2

---
## Operating Mode: \\( 0 < t < t\_1\\)

### Inductor Lr sees constant Vs voltage and the current increases linearly
--

### \\(i\_L(t)=\dfrac{V\_s}{L\_r} t \\)
--

### The moment that the current reaches to Io is:
--

### \\(t\_1 = \dfrac{I\_o L\_r}{V\_s}\\)

---
## Operating Mode: \\( t\_1 < t < t\_2\\)

### Diode is off, capacitor voltage starts building up:
--

### \\(v\_c(t) = V\_s - L\_r \dfrac{di\_L(t)}{dt}\\)
---

## Operating Mode: \\( t\_1 < t < t\_2\\)

### Differentiating and solving second order LC circuit (as in Ch9.2)
--

### \\( i\_L(t)=I\_o +\frac{V\_s}{Z\_o} sin \omega\_0 (t-t\_1) \\)

### \\( Z\_0 = \sqrt{\frac{L\_r}{C\_r}} \\)

### \\( \omega\_0 = \frac{1}{\sqrt{L\_r C\_r}} \\)
--

### \\( t\_2 - t\_1 = \frac{1}{\omega\_0} [sin^{-1}(\frac{-I\_0 Z\_0}{V\_s}) ]\\)

---

## Operating Mode: \\( t\_1 < t < t\_2\\)

### Capacitor voltage can be expressed as:

### \\( V\_c (t) = V\_s [1- cos (\omega\_0 (t-t\_1))]\\)

### which implies capacitor voltage can reach up to 2 Vs (a disadvantage of resonant converters)

---
## Operating Mode: \\( t\_2 < t < t\_3\\)

### As the inductor current reaches to zero at t2, the switch can be openced with no current (ZCS)
--

### Capacitor discharges with constant load current.

### \\( V\_c(t) =\frac{I\_0}{C\_r} (t\_2 -t) + V\_c(t\_2) \\)
--

### If Vc=0 at t3:

### \\(t\_3 - t\_2 = \frac{C\_r v\_c(t\_2)}{I\_o} = \frac{C\_r V\_s [1-cos(\omega\_o (t\_2 - t\_1))]}{I\_o}\\)

---
## Operating Mode: \\( t\_3 < t < T\\)

### In this interval switch is off (diode freewheeling)

### The length of this invertal directly controls the output voltage.

### The switching frequency should be adjusted so that t3 is less than period (T).

---
# Derivation of the Output Voltage
--

## Use energy balance (L-C are lossless)
--

### \\(V_o = V_s f_s [\dfrac{t\_1}{2}+ (t\_2 - t\_1)+ (t\_3-t\_2)]\\)
--

## \\(V_o < V_s \\) operates as a buck converter

## Output voltage is controlled by the switching frequency!

---

## Analysis of the Operating Modes
--

## Time internals are a function of output current
--

## Load changes switching frequency must be changed

---

# Example ( Hart 9-1)

---

# Resonant Switch Converter: Zero Voltage Switching

#### W. Hart., Power Electronics, Ch.9
--

<img src="./images/ee464/zvs.png" alt="Drawing" style="width: 800px;">
---

## Operating Mode: \\(t < 0\\)
--

### D1 off, switch ON, \\(i_{L} = I_o \\)

---

## Operating Mode: \\( 0 < t < t\_1\\)
--

### Switch opened, \\(v_C\\) start charging linearly

---

## Resonant Switch Converter: Zero Voltage Switching

---

## Operating Mode: \\( t\_1 < t < t\_2\\)
--

### When \\(v_C = V_s \\), the diode (D1) is forward biased

### LC resonant circuit start oscillating,

### When \\(v_C = 0 \\), the diode (Ds) turns on to carry iL. (which is negative)

---

## Resonant Switch Converter: Zero Voltage Switching

---

## Operating Mode: \\( t\_2 < t < t\_3\\)
--

### Ds is ON, \\(V_{L} = V_s \\), inductor current increases linearly

### Switch should be closed just after Ds turns on (zero voltage switching)

### When \\(i_{L} = I_o \\), D1 is off, and back to the initial position

---

## Initial Mode:  \\( t\_3 < t < T\\)
--

---

## Resonant Switch Converter: Zero Voltage Switching

---
## Resonant Switch Converter: Zero Voltage Switching

## Output voltage=?

---
## Resonant Switch Converter: Zero Voltage Switching

## Output voltage = Average of \\(v_x(t)\\)
--

### \\(v\_x(t) = V\_s (1-t/t\_1 ) \quad \\) for \\(0<t<t\_1\\)
--

### \\(v\_x(t) = 0 \quad \\) for \\(t\_1< t < t\_3\\)
--

### \\(v\_x(t) = V\_s  \quad \\) for \\(t\_3 < t <T\\)
--

### Calculate the average voltage

---
## Resonant Switch Converter: Zero Voltage Switching

## Output voltage
--

### \\(V\_o = \dfrac{V\_s}{T} [\dfrac{t\_1}{2}+(T-t\_3)]  \\) 
--

####or

### \\(V\_o = V\_s [ 1 - f\_s (t\_3 - \dfrac{t\_1}{2})]  \\) 
--

### Output voltage is controlled by varying fs

### \\(V\_o < V\_s \\), buck converter

---
## Resonant Switch Converter: Zero Voltage Switching

## Output voltage is controlled by varying fs

---

# Series Resonant Inverter

---

# Series Resonant Inverter

---

# Series Resonant Inverter

### Phasor equivalent circuit

---

# Series Resonant Inverter

### Frequency Response

---
# Series Resonant Converter
--

### Add a diode rectifier to the output of the series resonant inverter
--

---

# Variations of the Resonant Converters
--

### LLC Resonant Converter
--

---
## Resonant Converter (Wireless Power Transfer)

### [Qi Wireless Charging](https://www.wirelesspowerconsortium.com/qi/)

### [Multi-Coil Wireless Charger](https://www.nxp.com/design/designs/automotive-multi-coil-wireless-charging-transmitter:RDWCT-15WTXAUTO)

---
## Resonant Converter (Wireless Power Transfer)

### [BMW Electric Car Charger](https://newatlas.com/bmw-wireless-charging/54792/)

---
## Resonant Converter (Wireless Power Transfer)

### [Linearization and Control of Series-Series WPT](https://www.nxp.com/design/designs/automotive-multi-coil-wireless-charging-transmitter:RDWCT-15WTXAUTO)
---

## Various Configurations

### [For curious students: Overview of resonant circuits](https://www.mdpi.com/1996-1073/10/7/894/htm)

---
# [Dunning-Kruger Effect](https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect)
--

---
# [Dunning-Kruger Effect](https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect)

---
# [Dunning-Kruger Effect](https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect)

---
# Education in EEE

### [ODTÜ Elektrik size neler kattı?](https://www.youtube.com/playlist?list=PLI9c5vj6NMoJ5Afawulb9TckBB7O7r2Xn)

---

# The End

---
## You can download this presentation from: [keysan.me/ee464](http://keysan.me/ee464)

---
#Extras

---
# Alternative ZCS Converter

## Mohan Section 9.5

---
# Series Resonant Converter
--

### Add a diode rectifier to the output of the series resonant inverter
--

---
# Series Resonant Converter
--

### Simplified Equivalent Circuit

---

# Series Resonant Converter

### Continuous Conduction Mode  with \\(\omega\_s > \omega\_0\\)

---

# Series Resonant Converter

### Continuous Conduction Mode  with \\(\omega\_s > \omega\_0\\)

- ### iL is approximately sinusoidal

- ### Switches turn on at zero voltage (no turn-on losses)

- ### but they turn-off at non-zero current (turn-off losses exist)

---

# Series Resonant Converter

### Continuous Conduction Mode  with \\( \omega\_0/2 < \omega\_s < \omega\_0\\)

---

# Series Resonant Converter

### Continuous Conduction Mode  with \\( \omega\_0/2 < \omega\_s < \omega\_0\\)

- ### T+ conducts less than 180 degrees

- ### Switches turn on with finite voltage (turn-on losses exist)

- ### Switches turn-off with zero current (no turn-off losses)

- ### Turn-off occurs naturally, so thyristors can be used
---

# Series Resonant Converter

### Discontinuous Conduction Mode  with \\( \omega\_s < \omega\_0/2\\)

---

# Series Resonant Converter

### Discontinuous Conduction Mode  with \\( \omega\_s < \omega\_0/2\\)

- ### iL is zero for some time (discontinuous conduction)

- ### Switches turn on at zero current, with finite voltage

- ### Switches turn-off naturally with zero current (no turn-off losses)

- ### Thyristors can be used

- ### Disadvantage: Relatively large peak current in the circuit

---

# Variations of the Resonant Converters

### Parallel Resonant Converter

---

# Variations of the Resonant Converters

### Resonant DC Link Converter

---

# Variations of the Resonant Converters

### 3-Phase Resonant DC Link Converter