Datasheet LT1946A (Linear Technology) - 8
| Manufacturer | Linear Technology |
| Description | 2.7MHz Boost DC/DC Converter with 1.5A Switch and Soft-Start |
| Pages / Page | 12 / 8 — APPLICATIO S I FOR ATIO. Table 3. Bode Plot Parameters. Parameter. Value. … |
| Revision | S |
| File Format / Size | PDF / 326 Kb |
| Document Language | English |
APPLICATIO S I FOR ATIO. Table 3. Bode Plot Parameters. Parameter. Value. Units. Comment
Model Line for this Datasheet
Text Version of Document
LT1946A
U U W U APPLICATIO S I FOR ATIO
As with any feedback loop, identifying the gain and phase 1 ESR Zero: Z2 = contribution of the various elements in the loop is critical. 2 • π • ESR • COUT Figure 4 shows the key equivalent elements of a boost converter. Because of the fast current control loop, the 2 power stage of the IC, inductor, and diode have been V R IN L RHP Zero: Z3 = • replaced by the equivalent transconductance amplifier 2 2 • π • V • L OUT GMP. GMP acts as a current source where the output current is proportional to the VC voltage. Note that the maximum output current of G F MP is finite due to the current High Frequency Pole: P S 3 > limit in the IC. 3 From Figure 4, the DC gain, poles and zeroes can be Using the circuit of Figure 1 as an example, Table 3 shows calculated as follows: the parameters used to generate the bode plot shown in Figure 5. 2 =
Table 3. Bode Plot Parameters
Output Pole: P1 2 • π •R • C L OUT
Parameter Value Units Comment
RL 28 Ω Application Specific 1 COUT 2.2 µF Application Specific Error Amp Pole: P2 = 2•π •R •C R O C O 10 MΩ Not Adjustable CC 270 pF Adjustable 1 RC 27.4 kΩ Adjustable Error Amp Zero: Z1 = VOUT 12 V Application Specific 2 • π •R • C C C VIN 5 V Application Specific GMA 40 µmho Not Adjustable . DC Gain: A = 1 25 •G •R •G •R MA O MP L GMP 5 mho Not Adjustable VOUT L 2.2 µH Application Specific FS 2.7 MHz Not Adjustable – ESR 10 mΩ Not Adjustable GMP VOUT + ESR R From Figure 5, the phase when the gain reaches 0dB is L 122° giving a phase margin of 58°. This is more than + 1.250V COUT adequate. The cross-over frequency is 90kHz, which is V REFERENCE C R1 GMA about 30 times lower than the frequency of the right half – RC plane zero Z2. It is important that the cross-over frequency RO R2 be at least 3 times lower than the frequency of the RHP zero CC to achieve adequate phase margin. GMA: TRANSCONDUCTANCE AMPLIFIER INSIDE IC GMP: POWER STAGE TRANSCONDUCTANCE AMPLIFIER COUT: OUTPUT CAPACITOR RL: OUTPUT RESISTANCE DEFINED AS VOUT DIVIDED BY ILOAD (MAX) R1, R2: FEEDBACK RESISTOR DIVIDER NETWORK RO: OUTPUT RESISTANCE OF GMA RC: COMPENSATION RESISTOR CC: COMPENSATION CAPACITOR
Figure 4. Boost Converter Equivalent Model
sn1946a 1946afs 8
U U W U APPLICATIO S I FOR ATIO
As with any feedback loop, identifying the gain and phase 1 ESR Zero: Z2 = contribution of the various elements in the loop is critical. 2 • π • ESR • COUT Figure 4 shows the key equivalent elements of a boost converter. Because of the fast current control loop, the 2 power stage of the IC, inductor, and diode have been V R IN L RHP Zero: Z3 = • replaced by the equivalent transconductance amplifier 2 2 • π • V • L OUT GMP. GMP acts as a current source where the output current is proportional to the VC voltage. Note that the maximum output current of G F MP is finite due to the current High Frequency Pole: P S 3 > limit in the IC. 3 From Figure 4, the DC gain, poles and zeroes can be Using the circuit of Figure 1 as an example, Table 3 shows calculated as follows: the parameters used to generate the bode plot shown in Figure 5. 2 =
Table 3. Bode Plot Parameters
Output Pole: P1 2 • π •R • C L OUT
Parameter Value Units Comment
RL 28 Ω Application Specific 1 COUT 2.2 µF Application Specific Error Amp Pole: P2 = 2•π •R •C R O C O 10 MΩ Not Adjustable CC 270 pF Adjustable 1 RC 27.4 kΩ Adjustable Error Amp Zero: Z1 = VOUT 12 V Application Specific 2 • π •R • C C C VIN 5 V Application Specific GMA 40 µmho Not Adjustable . DC Gain: A = 1 25 •G •R •G •R MA O MP L GMP 5 mho Not Adjustable VOUT L 2.2 µH Application Specific FS 2.7 MHz Not Adjustable – ESR 10 mΩ Not Adjustable GMP VOUT + ESR R From Figure 5, the phase when the gain reaches 0dB is L 122° giving a phase margin of 58°. This is more than + 1.250V COUT adequate. The cross-over frequency is 90kHz, which is V REFERENCE C R1 GMA about 30 times lower than the frequency of the right half – RC plane zero Z2. It is important that the cross-over frequency RO R2 be at least 3 times lower than the frequency of the RHP zero CC to achieve adequate phase margin. GMA: TRANSCONDUCTANCE AMPLIFIER INSIDE IC GMP: POWER STAGE TRANSCONDUCTANCE AMPLIFIER COUT: OUTPUT CAPACITOR RL: OUTPUT RESISTANCE DEFINED AS VOUT DIVIDED BY ILOAD (MAX) R1, R2: FEEDBACK RESISTOR DIVIDER NETWORK RO: OUTPUT RESISTANCE OF GMA RC: COMPENSATION RESISTOR CC: COMPENSATION CAPACITOR
Figure 4. Boost Converter Equivalent Model
sn1946a 1946afs 8
