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MIC2155 Datasheet(PDF) 28 Page - Micrel Semiconductor |
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MIC2155 Datasheet(HTML) 28 Page - Micrel Semiconductor |
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28 / 33 page  Micrel, Inc. MIC2155/2156 May 2009 28 M9999-052709-A (408) 944-0800 formed by Co and it’s ESR, the slope of the gain curve changes from -40db/dec. to -20db/dec and the phase increases. The zero causes a 90° phase boost. Ceramic capacitors, with their smaller values of capacitance and ESR, push the zero and its phase boost out to higher frequencies, which allow the phase lag from the LC filter to drop closer to -180°. The system will be close to being unstable if the overall open loop gain crosses 0dB while the phase is close to -180°. If the output capacitance and/or ESR is high, the zero moves lower in frequency and helps to boost the phase, leading to a more stable system. The error amplifier is a type III which has two zeros, two poles and a pole at the origin. This type of error amplifier works well when Ceramic output capacitors make up the majority of COUT because it introduces an extra zero that helps improve phase margin. ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ω + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ω + ω ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ω + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ω + = 2 p s 1 1 p s 1 po s 2 z s 1 1 z s 1 ) s ( Gea where: 3 C 3 R 1 2 p 2 R 2 C 1 C 2 C 1 C 1 1 p 1 C 1 R 1 po 3 C ) 3 R 1 R ( 1 2 z 2 C 2 R 1 1 z × = ω ⋅ + × = ω × = ω ⋅ + = ω × = ω Figure 26 shows the bode plot of the error amplifier transfer function. Z1 1 2 π . R2 . C2 . Z2 1 2 π . R1 R3 () . C3 . P1 1 2 π . C2 C1 . C2 C1 . R2 . P2 1 2 π . R3 . C3 . 20 log R2 R1 . 2 1 2 1 0 C R Z ⋅ ⋅ ⋅ = π Figure 26. Type III Error Amplifier Gain/Phase Error Amplifier Design Procedure Step 1: Decide on the crossover frequency To maximize transient response, the open loop bandwidth should be made reasonably high. Initially, the bandwidth can be selected to be 1/10 of the output switching frequency. This may be improved once the design is built and measurements are made. An initial bandwidth of 100kHz for the 2155 and 60kHz for the 2156 are good choices. Step 2: Determine the gain required at the crossover frequency GBoost is how much gain boost is needed so the open loop transfer function crosses 0dB at the pre-determined crossover frequency. This can be measured by plotting the Gvd(s) transfer function or can be estimated with the following formula: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × × = fz fc fc fo V V H 1 G 2 M IN Boost Where: fo = LC filter resonant frequency fc= open loop bandwidth chosen in Step 1 fz = zero formed by Cout and its ESR H = voltage divider attenuation Vm=amplitude of the internal sawtooth ramp (Vm=1) Vin= Input voltage to the power supply |
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