Improving the Output Accuracy Over Temperature for RMS Power Detectors

Application Note 129
September 2010
Improving the Output Accuracy Over Temperature for
RMS Power Detectors
Andy Mo
INTRODUCTION
LTC5583 Temperature Compensation Design
Stable temperature performance is extremely important
in base-station designs because the ambient temperature can vary widely depending on the surroundings
and the location. Using high accuracy over temperature
RMS detectors can improve the power efficiency of the
base-station designs. The LTC5582 and the dual-channel
LTC5583 are a family of RMS detectors that offer excellent
stable temperature performance (from –40°C to 85°C) at
any frequency up to 10GHz for LTC5582, and 6GHz for
LTC5583. However, their temperature coefficients vary
with frequency, and without temperature compensation,
the error over temperature can be greater than 0.5dB.
As a result, sometimes it is necessary to optimize the
temperature compensation at different frequencies to
improve the accuracy to <0.5dB of error. In addition, the
temperature compensation can be implemented using only
two off chip resistors, with no external circuitry required.
LTC5583 includes two additional pins, RP1 that controls
the polarity of TC1, and RP2 which controls the polarity
of TC2. However, the magnitude of the temperature coefficients are the same with a fixed RT1, or RT2 value, only
polarity is flipped. Both channel A and channel B share
the compensation circuitry, therefore both channels are
controlled together.
ΔVOUT = TC1 • (TA – tNOM) + TC2 •
(TA – tNOM)2 + detV1 + detV2
(1)
Where TC1 and TC2 are the 1st and 2nd order temperature
coefficients respectively. TA is the actual ambient temperature, and tNOM is the reference room temperature, 25°C.
detV1 and detV2 are output voltage variation when RT1
and RT2 are not set to zero.
The method to calculate the resistor values for temperature
compensation is the same for both LTC5582, and LTC5583.
The two control pins are RT1, which sets TC1 (the 1st order
temperature compensation coefficient), and RT2 which sets
TC2 (the 2nd order temperature compensation coefficient).
Shorting RT1 and RT2 to ground conveniently turns off the
temperature compensation feature if not needed.
150
100
RP1 = OPEN
RP1 = SHORT
50
ΔVOUT (mV)
The change in output voltage is governed by the following
equation:
Figure 1 illustrates the change in VOUT as a function of
temperature from the 1st order temperature compensation. Only three resistor values are shown to illustrate
that increasing resistor values causes an increase in the
magnitude of the slope. The polarity of the slope is controlled by the RP1 pin.
0
–50
–100
–150
–50
10k
20k
30k
0
50
TEMPERATURE (°C)
100
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Figure 1. 1st Order ΔVOUT vs Temperature
Figure 4 illustrates the effect of 2nd order temperature
compensation on VOUT. The polarity of the curves is
controlled by RP2. The curvature depends on the resistor values. The overall effect is the summation of the 1st
order and 2nd order temperature compensation given by
equation 1.
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Application Note 129
LTC5583
Step 1. Estimate the temperature compensation needed in
dB, from Figure 5. For example, read the plot at an input
power of –25dBm, which is the middle of the dynamic
range. Multiply the linearity error in dB by 30mV/dB(typical
VOUT slope) to convert to mV.
VCC
RP1 OR RP2
OPEN OR
SHORT
Cold (–40°C) = 13mV or 0.43dB
Hot (85°C) = –20mV or –0.6dB
22.2k
This is the amount of output voltage adjustment required
over temperature.
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Figure 2. Simplified Schematic of Pins RP1 and RP2.
3
LINEARITY ERROR
RT1 = 0
RT2 = 0
2
LTC5583
RT1 OR
RT2
2.5
VOUT
1
2.0
0
1.5
–1
1.0
–2
–3
–70
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0.5
85°C
25°C
–40°C
–50
–30
–10
INPUT POWER (dBm)
VOUT (V)
250k
LINEARITY ERROR (dB)
VCC
3.0
10
0
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Figure 3. Simplified Schematic of Pins RT1, and RT2.
Step 2. Determine RP1 and RP2, and the solutions for 1st
and 2nd order compensation. To find the solutions, let a
= 1st order term, and b = 2nd order term. Set them up
so they satisfy the temperature compensation at –40°C
and 85°C.
80
60
RP2 = OPEN
ΔVOUT (mV)
40
20
0
–20
–40
–60
–80
–50
RP2 = SHORT
1k
4k
8k
0
50
TEMPERATURE (°C)
Figure 5. Uncompensated LTC5583 at 900MHz
100
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Figure 4. 2nd Order VOUT vs Temperature
Take an LTC5583 as an example at 900MHz input. The
first step is to measure the VOUT over temperature without
compensation. Figure 5 shows the uncompensated VOUT.
The Linearity error over temperature is referenced to the
slope and intercept point at 25°C. To minimize the output
voltage change with temperature, the linearity curve in red
(85°C) needs to be shifted down, and the linearity curve in
blue(–40°C) needs to be shifted up to align with the room
temperature in green, and overlap as much as possible.
What follows is a step by step design procedure.
a – b = 13mV
(2)
–a – b = –20mV
(3)
a = 16.5
(1st)
b = 3.5
(2nd)
The polarity of a and b in equation 2 and equation 3 are
determined by the polarity of the 1st order term and the 2nd
order term, such that their summation satisfy the 13mV at
cold (–40°C), and –20mV at hot (85°C) adjustment. Refer
to Figure 6. 1st order term and 2nd order term can be either
positive or negative. So there are total of 4 combinations
possible. In this case, only when both terms are negative
will their sum satisfy the required compensation.
Figure 7 shows the 1st and 2nd order compensation required at –40°C and 85°C. Notice the polarity of the 1st
order and 2nd order compensation are negative such that
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Application Note 129
1.6
ΔV
1.2
30
0.8
60
ΔT
+
20
RP1 = 0
0.4
detV1
10
detV1
–10
0
0
–0.4
RP1 = 0PEN
–0.8
detV1 (mV)
–65
TC1 (mV/°C)
b = +TC2ΔT2
–
40
TC1
+ a = +TC1ΔT
a = –TC1ΔT
–20
–
–1.2
b = –TC2ΔT2
ΔT = (TA – tNOM)
tNOM = 25°C
–1.6
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5
10
15
15
–0.5
–1.0
10
–1.5
5
–2.0
0
–2.5
–3.0
–10
–3.5
–15
–20
–40
–20
0
20
40
TEMPERATURE (°C)
Figure 8. 1st Order Temperature Compensation Coefficient TC1
vs External RT1 Values
–4.0
1ST ORDER
2ND ORDER
60
80
–40
35
30
–4.5
16
200
TC2
12
100
detV2
RP2 = OPEN
4
50
0
0
–4
detV2
RP2 = 0
–50
–8
–100
–12
–16
–150
TC2
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Figure 7. Solutions for the Temperature Compensation
150
8
detV2 (mV)
–5
20
25
RT1 (kΩ)
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TC2 (μV/°C2)
0
2ND ORDER ΔVOUT (mV)
1ST ORDER ΔVOUT (mV)
Figure 6. Polarity of 1st and 2nd Order Solutions
20
–30
TC1
0
1
2
3
4 5 6
RT2 (kΩ)
7
8
–200
10
9
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when both curves are added, their sum produces the required adjustment to VOUT. Consequently, TC1 and TC2 are
negative, and RP1 and RP2 are determined from Figure 8
and Figure 9. Notice the values of the two solutions add
up to approximately 13mV at –40°C, and –20mV at 85°C.
RP1 = open
RP2 = short
Step 3. Calculate the temperature coefficients at one of
the temperature extremes and determine resistor values
RT1 and RT2, using Figures 8 and 9.
a = 16.5 = TC1 • (85 – 25); TC1 = 0.275mV/°C
RT1 = 11k (from Figure 8)
Figure 9. 2nd Order Temperature Compensation Coefficient
TC2 vs External RT2 Values
tions. However, for some applications where even better
accuracy is needed, a 2nd iteration can be performed to
further improve the temperature performance. To simplify
the calculation, detV1 and detV2 terms are ignored because
they are not dependent on temperature. As a result, the
solutions are not precise. However, it is very helpful in
improving the accuracy over temperature, as shown here.
2nd Iteration Calculation
Step 1. Find the compensation needed from Figure 10,
using the same method in first iteration.
b = 3.5 = TC2 • (85 – 25)2; TC2 = 0.972μV/°C2
Cold (–40°C) = –3mV or –0.1dB
RT2 = 499Ω (from Figure 9)
Hot (85°C) = –3mV or –0.1dB
Figure 10 shows the LTC5583 performance over temperature
for one of the two output channels. Notice an improvement
to the temperature performance from uncompensated VOUT,
from Figure 5. This may be satisfactory for most applica-
Add the new values to the 1st iteration
Cold (–40°C) = –3mV + 13mV = 10mV
Hot (85°C) = –3mV – 20mV = –23mV
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Application Note 129
RT1 = 11k
RT2 = 499Ω
LINEARITY ERROR
VOUT
1
2.0
1.0
–50
–30
–10
INPUT POWER (dBm)
10
VOUT
1
3.0
2.5
2.0
0
1.5
–1
1.0
0.5
–2
0
–3
–70
0.5
85°C
25°C
–40°C
–50
–30
–10
INPUT POWER (dBm)
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VOUT (V)
–1
–3
–70
2
2.5
1.5
85°C
25°C
–40°C
RT1 = 11k
RT2 = 953Ω
LINEARITY ERROR
0
–2
3
VOUT (V)
LINEARITY ERROR (dB)
2
3.0
LINEARITY ERROR (dB)
3
10
0
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Figure 10. Temperature Compensated LTC5583 Output
After 1st Iteration
Figure 11. Temperature Compensated LTC5583 Output
After 2 Iterations.
Repeat steps 2 and 3 to calculate the RT1 and RT2 values.
the polarity has been predetermined. Both TC1 and TC2
are negative. Refer to Table 2 for RT1 and RT2 values at
other frequencies. The compensation coefficients shown
in Figure 8 and Figure 9 are different for LTC5582. Refer
to data sheet for additional information.
RT1 = 11k
RT2 = 953Ω
RP1 = open
Table 2. Recommended RT1 and RT2 Values of LTC5582 for
Optimal Temperature Performance at Various Frequencies
RP2 = short
The performance results are shown in Figure 11 after two
iterations. Over temperature, the dynamic range is 50dB
with 0.2dB of linearity error, and 56dB of dynamic range
with 1.0dB of linearity error. Refer to Table 1 for temperature
compensation values at other frequencies.
Tabel 1. Recommended Settings and Resistor Values for
LTC5583 for Optimal Temperature Performance at Various
Frequencies
FREQUENCY (MHZ)
RT1 (kΩ)
RT2 (kΩ)
450
12
2
800
12.4
1.4
880
12
2
2000
0
2
2140
0
2
2600
0
1.6
2700
0
1.6
FREQUENCY (MHz)
RP1
RP2
RT1 (kΩ)
RT2 (kΩ)
3000
0
1.6
450
Open
0
11.5
1.13
3600
0
1.6
880
Open
0
11.5
1.13
5800
0
3
900
Open
0
11
0.953
7000
10
1.43
1800
Open
0
12.1
1.5
8000
10
1.43
2140
Open
0
9.76
1.1
10000
10
3
2300
Open
0
10.5
1.43
2500
Open
0
10.5
1.43
2700
Open
0
8.87
1.21
This iteration process can be repeated over and over again
to further increase the accuracy. This will allow the designer
to dial in the compensation as accurately as needed for
most applications.
LTC5582 Single Detector
The method to calculate the LTC5582 compensation
values for RT1 and RT2 is the same, only easier because
Conclusion
LTC5582 and LTC5583 offer excellent temperature performance with only two external compensation resistors.
The procedure to calculate the compensation resistors is
simple, and can be reiterated for even better performance.
The example shown here is for LTC5583 at 900MHz RF
input, but the method can be applied to LTC5582 and
LTC5583 at any frequency within the limits of the IC. The
performance over temperature is fairly consistent from
part to part. The resulting performance provides accuracy
over temperature with less than 1% of output voltage.
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