
关键词: current sense amplifier, automotive antenna, antenna power supply, remote antenna power supply, remote antenna power, phantom power, radio antenna lna, active antenna detection, antenna diagnostics
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How to Calculate the Operating Windows for a Remote Antenna CurrentSense Amplifier and Switch
By: 
Robert Regensburger, Automotive Specialist, Automotive Product Definitions, Maxim Integrated, Germany 

Abstract: This application note helps designers choose the correct external components to ensure that automobile antennadetection circuitry meets performance objectives. A calculator details how to specify the critical external components for the MAX16913/MAX16913A remote antenna currentsense amplifiers and switches. The calculator also determines the device's operational windows and analog output voltage accuracy. An example calculation is given.
Introduction
The
MAX16913/MAX16913A (
Figure 1) are precision currentsense amplifiers (CSAs) and switches that provide phantom power to remote radio antennas in automotive applications. In addition, they provide shortcircuit protection, currentlimit protection, and openload detection. To ensure that their antenna detection circuitry meets performance objectives, the design engineer must choose the correct external components for a design.
When working with CSAs and switches for antenna applications, the designer must often determine the operational windows for an open load, normal operation, a short circuit, and current limiting (
Figure 2). In addition, the accuracy of the CSA's analog output voltage must also be verified.
Figure 1. Typical operating circuit of the MAX16913A remote antenna CSA and switch.
Figure 2. Operation ranges for these CSAs.
This application note presents a calculator that shows how to determine the proper sense resistor and the resistordivider for setting the openload threshold (detection range) tolerance. It considers the tolerances of both the external components and the MAX16913/MAX16913A, and then calculates the appropriate tolerance window ranges for optimal performance. The calculator is available
here, and an example calculation follows.
Calculate the Required Sense Resistor
Ideally the maximum operating current develops the fullscale sense voltage across the currentsense resistor, R
_{SENS} (Figure 1). Calculate the maximum value for R
_{SENS} so that the differential voltage across IN and SENS does not exceed the minimum fullscale sense voltage (87mV)*:
Where V
_{DIFF(MIN)} = V
_{IN}  V
_{SENSE} = 87mV (min) at the maximum guaranteed output current, I
_{LOAD(FULLSCALE)} (Figure 2).
However, resistors always have tolerances, so the actual resistor value can be higher by its tolerance rating, thus causing the device to detect a short circuit too early. After considering the resistor's tolerance rating, the nominal maximum resistor value can be calculated:
Where R
_{SENS(MAX)} is the maximum sense resistor calculated above, and R
_{SENSTOLERANCE} is the tolerance rating of the resistor. Remember that exact values for the calculated sense resistor may not be available. If that is the case, choose the closest smaller value for R
_{SENS(MAX)(NOM)} and use that to calculate R
_{SENS_P(NOM)}. Alternatively serial or parallel combinations of standard resistors can be used to attain the optimal sense resistor.
Calculate the ShortCircuit CurrentDetection Window
The nominal sense resistor has been chosen. Now the typical current through the sense resistor, when a short circuit is detected, can be calculated as follows:
Where V
_{SC(TYP)} is the typical value of the shortcircuit voltage threshold (100mV)* and R
_{SENS_P(NOM)} is the sense resistor selected above.
However, as V
_{SC} and R
_{SENS} have uncorrelated tolerances (i.e., have minimum and maximum values that vary independently of each other), an additional error has to be considered. So the worstcase shortcircuit, currentdetection window is:
And
Where V
_{SC(MIN)} is the minimum value of the shortcircuit voltage threshold (87mV)* and V
_{SC(MAX)} is the maximum value (110mV).* Therefore:
R_{SENS_P(MAX)} 
= R_{SENS_P(NOM)} + its tolerance rating + R_{SENS_P(MIN)} 

= R_{SENS_P(NOM)}  its tolerance rating 
The shortcircuit flag (activelow SC) will thus go low when the current is in the range between I
_{SC(MIN)} and I
_{SC(MAX)}.
Calculate the CurrentLimit Range
Analogous to the shortcircuit currentdetection window, the currentlimit range is typically:
Where V
_{LIM(TYP)} is the typical value of the currentlimit threshold voltage between IN and SENS (200mV),* and R
_{SENS_P(NOM)} is the sense resistor selected.
Considering that V
_{LIM} and R
_{SENS} have uncorrelated tolerances, the worstcase currentlimit range through the sense resistor can be calculated:
And
Where V
_{LIM(MIN)} is the minimum value of the voltage between IN and SENS (173mV),* and V
_{LIM(MAX)} is the maximum value (225mV).*
Calculate the OpenLoad Detection Window
This procedure differs for the MAX16913 and MAX16913A.
For the MAX16913
The openload detection threshold (activelow OL) for the MAX16913 is set internally to V
_{OLT} = 0.66V.* The associated current range using a 1Ω resistor is specified in the data sheet as 10mA (min), 20mA (typ), and 30mA (max). These values include the tolerance of the openload comparator, the gain amplifier, and the external sense resistor (1Ω).
To determine the openload detection window using a different sense resistor, first the given current levels must be converted to a voltage:
Then using the values calculated above, the typical value of the openload current detection threshold calculates to:
Where V
_{OLT(TYP)} is the typical value of the openload detectionthreshold voltage calculated above, and R
_{SENS_P(NOM)} is the sense resistor selected.
Considering also the tolerances of the openload current threshold and the tolerance of the sense resistor, then the current range for openload detection calculates to:
And
Where V
_{OLT(MIN)} and V
_{OLT(MAX)} are the minimum and maximum values of the openload detectionthreshold voltage; R
_{SENS_P(MIN)} and R
_{SENS_P(MAX)} are the minimum and maximum values of the sense resistor calculated above.
The worstcase openload detection window lies between I
_{OL(MIN)} and I
_{OL(MAX)}.
For the MAX16913A
The openload threshold for the MAX16913A can be adjusted externally with a resistordivider between REF, OLT, and GND. Therefore, the first task is to specify the external resistordivider.
Specify the External ResistorDivider
To begin, choose the voltage needed on the OLT pin to set the desired nominal OL threshold (at the OLT pin, Figure 1) using the following formula:
V_{OLT}(V) = I_{OLT}(A) × R_{SENS}(Ω) × A_{V}(V/V) + 0.133 × V_{REF}
Where AV is the (V
_{IN}  V
_{SENS}) to V
_{AOUT} gain (13V/V) and V
_{REF} is the REF pin voltage (3V).* The ratio of the external resistors on the OLT pin can then be calculated using the following equation:
R_{2}/R_{1} = V_{OLT}/(V_{REF} × (1  V_{OLT}/V_{REF}))
Where V
_{REF} is the voltage on the REF pin (3V). An arbitrary standard value can now be chosen for R
_{1} or R
_{2}, and the other resistor value can then be calculated (Figure 1). However, ensure that the impedance of the resistordivider does not load the internal reference voltage excessively.
Determine the OpenLoad ThresholdVoltage Range
The standard resistor values for R1 and R2 have now been defined. Next, considering the uncorrelated tolerances of V
_{REF} and the resistors R1 and R2, the worstcase voltage range for the openload pin, V
_{OLTw}, can be calculated:
And
Where R
_{2(MIN)} is the nominal value of R
_{2} minus its tolerance value. This can be restated as R
_{2(MIN)} = R
_{2}  (R
_{2} × (R
_{2TOL}[%]/100%)) and R
_{1(MAX)} is the nominal value of R
_{1} plus the tolerance.
Determine the WorstCase, OpenLoad CurrentDetection Window
At this point V
_{OLTw(MIN)} and V
_{OLTw(MAX)} have been calculated. Now taking into consideration the tolerances of the REF output voltage, V
_{REF}, the sense resistor, R
_{SENS_P(NOM)}, and the gain, AV, the worstcase current window when open load is detected (activelow OL) can be calculated:
And
Where V
_{OLTw(MIN)}, V
_{OLTw(MAX)}, R
_{SENS_P(MIN)}, and R
_{SENS_P(MAX)} have been calculated above; A
_{V} is the (V
_{IN}  V
_{SENS}) to V
_{AOUT} gain which has minimum and maximum values of 12.87 and 13.13, respectively*; and V
_{REF(MIN)} and V
_{REF(MAX)} are the minimum and maximum values of the REF pin voltage (2.7V and 3.3V).*
Evaluate the Current Through R_{SENS} by Measuring Voltage on A_{OUT}
A_{OUT} Accuracy
With a given sense resistor, R
_{SENS}, and a defined current through it, I
_{SENS}, then the worstcase range of voltage values measured at the currentsense amplifier's output, A
_{OUT} (e.g., a microcontroller's analogtodigital converter (ADC)), can now be calculated. Consider also the uncorrelated tolerances of A
_{OUT_Z} and the sense resistor, R
_{SENS}. Therefore:
V_{AOUT(MIN)}(V) = A_{OUT_Z(MIN)}(V) + A_{V(MIN)}(V/V) × R_{SENS(MIN)}(Ω) × I_{SENS}(A)
And
V_{AOUT(MAX)}(V) = A_{OUT_Z(MAX)}(V) + A_{V(MAX)}(V/V) × R_{SENS(MAX)}(Ω) × I_{SENS}(A)
Where A
_{V(MIN)} is 12.87V and A
_{V(MAX)} is 13.13V;* and A
_{OUT_Z(MIN)} and A
_{OUT_Z(MAX)} are the minimum and maximum values of the A
_{OUT} zerocurrent output voltage (340mV)* (460mV);* and R
_{SENS(MIN)} and R
_{SENS(MAX)} are the sense resistor plus/minus its tolerance.
Stated in other words, the sensed current produces a worstcase A
_{OUT} voltage variation between V
_{AOUT(MIN)} and V
_{AOUT(MAX)}.
Taking the above worstcase voltage levels and using a microcontroller's software to calculate those voltages back to a current, one can calculate:
And
Where V
_{AOUT(MIN)} and V
_{AOUT(MAX)} have been calculated above; AV is the (V
_{IN}  V
_{SENS}) to V
_{AOUT} gain (13V/V);* A
_{OUT_Z(TYP)} is the typical value of the A
_{OUT} zerocurrent output voltage (400mV);* and R
_{SENS} is the nominal value of the sense resistor.
Thus when the analog output voltage is used to measure a certain current through the sense resistor, the microcontroller's ADC gives a current value between I
_{EVALUATED(MIN)} and I
_{EVALUATED(MAX)}.
The current measurement tolerance, I
_{TOL}, is:
Example Calculations
For these example calculations we assume an antenna phantom supply application where the upper end of the normal operation window (I
_{LOAD(FULLSCALE)}) is at 100mA. Then the maximum value of the sense resistor required is:
When using a resistor with a 1% tolerance, the maximum sense resistor that can be selected is:
As a 0.861Ω resistor is not available as a standard value, we select the next smaller value from the E96 series for R
_{SENSP(NOM)} = 0.845Ω. We use this value for our subsequent calculations.
Next, the typical current value for shortcircuit detection can be calculated:
As previously shown, the minimum and maximum values for the shortcircuit currentdetection window lie between I
_{SC(MIN)} and I
_{SC(MAX)}. To calculate these values, we first need the minimum and maximum values of the selected sense resistor.
This allows us to derive the limits of the shortcircuit currentdetection window:
And
Analogous to the shortcircuit currentdetection window, the typical value of the currentlimit range is:
Considering the tolerances, the minimum and maximum values for the currentlimit range lie between I
_{LIM(MIN)} and I
_{LIM(MAX)}:
And
Now for the MAX16913, the typical value for the openload detection threshold is:
Including the tolerances, the minimum and maximum values are:
And
Turning now to the MAX16913A, we assume an application where the maximum current value of the openload detection window is at 30mA. Therefore, the maximum voltage value for the center point of the resistordivider is:
Next we pick a standard resistor for R2 from the E96 series, 90.9kΩ (1%), and calculate its maximum value:
The minimum resistor value for the upper resistor of the divider is then:
The nominal value, assuming also a 1% tolerance, is:
The closest higher standard value to be selected with the same tolerance is R1 = 392kΩ. Considering also its tolerance, we calculate:
And the minimum value for R2 is:
Continuing with these values, the openload thresholdvoltage range is:
And
Then the worstcase current window for the openload detection of the MAX16913A is:
And
To evaluate the analog output, A
_{OUT}, accuracy, we assume the same sense resistor selected above (0.845Ω) and evaluate the accuracy at a load current of 100mA. At this current, the minimum and maximum values of the A
_{OUT} voltage are between:
V_{AOUT(MIN)}(V) = A_{OUT_Z(MIN)}(V) + A_{V(MIN)}(V/V) × R_{SENS(MIN)}(Ω) × I_{SENS}(A) = 340mV + 12.87(V/V) × 0.837Ω × 100mA = 1.417V
And
V_{AOUT(MAX)}(V) = A_{OUT_Z(MAX)}(V) + A_{V(MAX)}(V/V) × R_{SENS(MAX)}(Ω) × I_{SENS}(A) = 460mV + 13.13(V/V) × 0.853Ω × 100mA = 1.58V
Taking these voltages and calculating back as the microcontroller's software would do (i.e., taking the typical values from the data sheet), we derive an evaluated current between:
And
The worstcase tolerance of the measured current can then be up to:
*For more details on these calculations, see the data sheet for the MAX16913/MAX16913A.
© Jun 24, 2011, Maxim Integrated Products, Inc.

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APP 4798: Jun 24, 2011
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