SLLA549 July 2021 TCAN4550 , TCAN4550-Q1 , TCAN4551-Q1

7 Calculate the Negative Resistance

Figure 7-1 Negative Resistance Measurement Test Setup

The typical transconductance (gm) of the TCAN455x Pierce Oscillator circuit is 6.6 mS

Calculate the negative resistance by the following formula:

Equation 12.

R_{n e g_c a l c} = - \frac{g_{m}}{{ω^{2} \times (2 \times C_{L o a d})}^{2}}

Measure the negative resistance by inserting a series resistor (Rs) in between the crystal pin and the CL1 external load capacitor on the amplifier output (OSC1) side of the crystal. Monitor the crystal oscillation frequency and increase the resistor value until the oscillation stops. The total negative resistance is equal to the Load Resistance plus the added series resistance.

This requires the crystal to be removed from the PCB so that the resistor can be inserted, while maintaining the electrical connections with the other components with as little additional inductive, resistive, and capacitive impact as possible.

A cermet potentiometer, which is ceramic based and non-inductive, could be used instead of replacing the series resistors with discrete resistors of increasing value. However, the potentiometer chosen should have low capacitance so that the capacitive reactance does not alter the total load resistance and load capacitance of the circuit in a significant way. Once the oscillation stops, the resistance across the potentiometer can be measured.

The amount of negative resistance in the system can be calculated by the following formula:

Equation 13.

(R_{n e g}) = R_{S e r i e s} + R_{L o a d}

Compare the previously calculated negative resistance that was calculated with the typical transconductance value gm, to the value calculated using the resistor measurement method. If the values do not match, adjustments may be needed to the transconductance (gm), frequency (f_s), R_Load, or C_Load values. Check the R_Load and C_Load calculations for accuracy and solve for a more accurate transconductance value gm.

It is important that there is enough negative resistance to overcome changes in the circuit as a result of component tolerance differences on key parameters and shifting values due to environmental conditions such as temperature and humidity. If there is not enough margin between the amount of negative resistance and the load resistance, there is a chance the oscillation in the circuit can stop or fail to start when power is applied to the circuit. Verify the magnitude of the negative resistance is 3 to 5 times larger than the Load Resistance by the following formula. This is commonly referred to as the Safety Factor.

Equation 14.

R_{S a f e t y} = \frac{| - R_{n e g} |}{R_{L o a d}}

If the negative resistance margin is too low, the load resistance R_Load is too large for ensured safe operation of the oscillation circuit. The load capacitance may need to be adjusted by using larger external capacitor values in order to lower the total load resistance.

If the capacitors are adjusted to improve the negative resistance margin, the oscillation frequency will shift. Re-measure the oscillation frequency to ensure it is still within specification. Re-calculate the load capacitance and load resistance values that will be needed in other calculations.

If the external load capacitors cannot be adjusted to an appropriate level, then a crystal with more appropriate motional properties may be needed.

It is important to reduce the parasitic PCB capacitance C_{PCB_Stray} as much as possible with proper layout techniques to allow greater margin and room for adjustment with different values of components.