R2J20701NP_08 RENESAS [Renesas Technology Corp], R2J20701NP_08 Datasheet - Page 15

• Manufacturer Part Number: R2J20701NP_08
• Description: Peak Current Mode Synchronous Buck Controller with Power MOS FETs
• Manufacturer: RENESAS [Renesas Technology Corp]

R2J20701NP
Design example
Specification: L = 360 nH, Co = 600 µF, Fsw = 500 kHz, Vin = 12 V, Vout = 1.8 V, R1 = 2 kΩ, R2 = 1 kΩ,
1. Flat-band gain of error amplifier
2. Selecting the Cf value to determine the frequency of the zero
REJ03G1459-0400 Rev.4.00 Jun 30, 2008
Page 15 of 27
The flat-band gain is; Af = Rf / (R1 // R2) / 2 × {R2 / (R1 + R2)}
In the Bode plot, the total gain should be less than 1 (0 dB) at the switching frequency.
The total gain at Fsw (= Asw) depends on the flat-band gain, so Af should be expressed as follows.
In the typical way, the value chosen for Asw is in the range from 0.1 to 0.5, since this produces a stable control loop.
The transient response will be faster if a larger Asw is adopted ,but the system might be unstable.
We choose 0.2 for Asw in the example below.
Therefore, we select a value of 62 kΩ for Rf.
The frequency of the zero established by Cf and Rf is about ten times the frequency of the pole for the power stage
and modulator.
We must start with the dc gain of the power stage and modulator.
Here VCS0 is the peak ac voltage on the CS pin when the load current is zero, thus
Vout
R1
R2
Hence, Rf = 2 × Af × R1 ……(1)
Af = Asw × 2 π × Fsw × Co × RCS / Nt ……(2)
Af = 0.2 × 2 π × 500 kHz × 600 µF × 750 Ω / 18500 = 15.283
Rf = 2 × 15.283 × 2 kΩ = 61.132 kΩ
A0 =
VCS0 = 0.5 × RCS × (Vin – Vout) × Vout / (L × Vin × Fsw) / 18500 ……(4)
Here, Nt = Idh / Ics = 18500
SQRT {Vin
RCS = 750 Ω
= 0.5 × 750 Ω × (12 V – 1.8 V) × 1.8 V / (360 nH × 12 V × 500 kHz) / 18500
= 0.172 V
2
2
Rf
8
FB
Nt / RCS
L
Vin
Figure 3 Error Amplifier Compensation
0.6 V reference
Cf
Fsw
L
Vin
(VCS0
Fsw
EO
Nt / RCS) }
50 k
50 k
Amplifier output: to current-sense comparator
(3)