Calculating Maximum Power Delivery to Load in Current Steering DACs
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•
Calculate the peak-to-peak voltage at the output of the DAC
–
Vdac
p-p
= I
FS
* R
–
Where R is the total impedance seen by the DAC and I
FS
is the full-scale
output current
•
Find voltage at load by dividing by the sqrt of the impedance ratio
–
Vload
p-p
= Vdac
p-p
/ sqrt(N
Imp
)
–
Where sqrt(Nimp) = 2 for 4:1 trans, 1.414 for 2:1 trans, 1 for 1:1 trans
•
Convert peak-to-peak voltage to rms voltage
–
Vload
rms
= Vload
p-p
/ (2 * sqrt(2) )
•
Calculate power DELIVERED to the load
–
P
load
= (Vload
rms
)
2
/ R
L
–
R
L
is the impedance after the transformer, probably 50 ohms such as in
the case of a spectrum analyzer hooked up to the transformer output
•
Convert power to dBm
–
P
dBm
= 10 * log(P
load
/ 1 mW)
2
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Vdac
p-p
= (20 mA) * ((50+50) // 100 // 50) = 500 mV (25 ohm total load)
Vload
p-p
= 500 mV / sqrt(1) = 500 mV
Vload
rms
= 500 mV / (2 * sqrt(2) ) = 176.8 mV
P
load
= (176.8 mV)
2
/ 50 = 625.2 uW (spectrum analyzer = 50 ohm load)
P
d
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m
=
1
0
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/
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)
=
-
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Vdac
p-p
= (20 mA) * ((50+50) // (2*50)) = 1 V (50 ohm total load)
Vload
p-p
= 1 V / sqrt(2) = 707.2 mV
Vload
rms
= 707.2 mV / (2 * sqrt(2) ) = 250 mV
P
load
= (250 mV)
2
/ 50 = 1.25 mW (spectrum analyzer = 50 ohm load)
P
d
B
m
=
1
0
*
l
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g
(
1
.
2
5
m
W
/
1
m
W
)
=
0
.
9
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4
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Vdac
p-p
= (20 mA) * ((100+100) // (4*50)) = 2 V (100 ohm total load)
Vload
p-p
= 2 V / sqrt(4) = 1 V
Vload
rms
= 1 V / (2 * sqrt(2) ) = 353.6 mV
P
load
= (353.6 mV)
2
/ 50 = 2.5 mW (spectrum analyzer = 50 ohm load)
P
d
B
m
=
1
0
*
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2
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5
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W
/
1
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)
=
3
.
9
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5
In the process of calculating the maximum power delivered to the load for current steering DACs, several steps are involved, such as determining the peak-to-peak voltage at the DAC output, converting it to RMS voltage, calculating power delivered to the load, and converting power to dBm. Examples with different transformer ratios illustrate the calculations and power values obtained. Understanding these calculations is essential for optimizing power delivery in systems utilizing DACs.
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Presentation Transcript
Calculating maximum power delivered to load for current steering DACs 1
Calculations Calculate the peak-to-peak voltage at the output of the DAC Vdacp-p = IFS * R Where R is the total impedance seen by the DAC and IFS is the full-scale output current Find voltage at load by dividing by the sqrt of the impedance ratio Vloadp-p = Vdacp-p / sqrt(NImp) Where sqrt(Nimp) = 2 for 4:1 trans, 1.414 for 2:1 trans, 1 for 1:1 trans Convert peak-to-peak voltage to rms voltage Vloadrms = Vloadp-p / (2 * sqrt(2) ) Calculate power DELIVERED to the load Pload = (Vloadrms)2 / RL RL is the impedance after the transformer, probably 50 ohms such as in the case of a spectrum analyzer hooked up to the transformer output Convert power to dBm PdBm = 10 * log(Pload / 1 mW) 2
Example 1:1 transformer Vdacp-p = (20 mA) * ((50+50) // 100 // 50) = 500 mV (25 ohm total load) Vloadp-p = 500 mV / sqrt(1) = 500 mV Vloadrms = 500 mV / (2 * sqrt(2) ) = 176.8 mV Pload = (176.8 mV)2 / 50 = 625.2 uW (spectrum analyzer = 50 ohm load) PdBm = 10 * log(625.2 uW / 1 mW) = -2.04 dBm 3
Example 2:1 transformer Vdacp-p = (20 mA) * ((50+50) // (2*50)) = 1 V (50 ohm total load) Vloadp-p = 1 V / sqrt(2) = 707.2 mV Vloadrms = 707.2 mV / (2 * sqrt(2) ) = 250 mV Pload = (250 mV)2 / 50 = 1.25 mW (spectrum analyzer = 50 ohm load) PdBm = 10 * log(1.25 mW / 1 mW) = 0.969 dBm 4
Example 4:1 transformer Vdacp-p = (20 mA) * ((100+100) // (4*50)) = 2 V (100 ohm total load) Vloadp-p = 2 V / sqrt(4) = 1 V Vloadrms = 1 V / (2 * sqrt(2) ) = 353.6 mV Pload = (353.6 mV)2 / 50 = 2.5 mW (spectrum analyzer = 50 ohm load) PdBm = 10 * log(2.5 mW / 1 mW) = 3.98 dBm 5
