Frequency (MHz) FIGURE 1.7 Typical graph of impedance as a percentage of dc resistance versus frequency for film resistors. The smaller the diameter of the resistor the better is its frequency response. Most high-frequency resistors have a length to diameter ratio between 4: 1 to 10: 1. Dielectric losses are kept to a minimum by proper choice of base material Voltage Coefficient of Resistance Resistance is not always independent of the applied voltage. The voltage coefficient of resistance is the change in resistance per unit change in voltage, expressed as a percentage of the resistance at 10% of rated voltage. The voltage coefficient is given by the relationship Voltage coefficient 100(R1-R2) (18) R2(V-V2) where R, is the resistance at the rated voltage Vi and R2 is the resistance at 10% of rated voltage V2. Resistors exhibit electrical noise in the form of small ac voltage fluctuations when dc voltage is applied. Noise in a resistor is a function of the applied voltage, physical dimensions, and materials. The total noise is a sum of Johnson noise, current flow noise, noise due to cracked bodies, resistors the noise can also be caused by the jumping of a moving contact over turns and by an imperfect electrical path between the contact and resistance element. The Johnson noise is temperature-dependent thermal noise(Fig. 1. 8). Thermal noise is also called"white noise" because the noise level is the same at all frequencies. The magnitude of thermal ERMs (V), is dependent on the resistance value and the temperature of the resistance due to thermal agitation kRT△f where ERMs is the root-mean-square value of the noise voltage(V), R is the resistance(]2), K is the Boltzmann constant(1.38x 102J/K), Tis the temperature( K), and Af is the bandwidth(Hz)over which the noise energy Figure 1. 8 shows the variation in current noise versus voltage frequency. Current noise varies inversely with frequency and is a function of the current flowing through the resistor and the value of the resistor. The magnitude of current noise is directly proportional to the square root of current. The current noise magnitude is usually expressed by a noise index given as the ratio of the root-mean-square current noise voltage(ERMs© 2000 by CRC Press LLC The smaller the diameter of the resistor the better is its frequency response. Most high-frequency resistors have a length to diameter ratio between 4:1 to 10:1. Dielectric losses are kept to a minimum by proper choice of base material. Voltage Coefficient of Resistance Resistance is not always independent of the applied voltage. The voltage coefficient of resistance is the change in resistance per unit change in voltage, expressed as a percentage of the resistance at 10% of rated voltage. The voltage coefficient is given by the relationship (1.8) where R1 is the resistance at the rated voltage V1 and R2 is the resistance at 10% of rated voltage V2. Noise Resistors exhibit electrical noise in the form of small ac voltage fluctuations when dc voltage is applied. Noise in a resistor is a function of the applied voltage, physical dimensions, and materials. The total noise is a sum of Johnson noise, current flow noise, noise due to cracked bodies, and loose end caps and leads. For variable resistors the noise can also be caused by the jumping of a moving contact over turns and by an imperfect electrical path between the contact and resistance element. The Johnson noise is temperature-dependent thermal noise (Fig. 1.8). Thermal noise is also called “white noise” because the noise level is the same at all frequencies. The magnitude of thermal noise, ERMS (V), is dependent on the resistance value and the temperature of the resistance due to thermal agitation. (1.9) where ERMS is the root-mean-square value of the noise voltage (V), R is the resistance (W), K is the Boltzmann constant (1.38 ¥ 10–23 J/K), T is the temperature (K), and Df is the bandwidth (Hz) over which the noise energy is measured. Figure 1.8 shows the variation in current noise versus voltage frequency. Current noise varies inversely with frequency and is a function of the current flowing through the resistor and the value of the resistor. The magnitude of current noise is directly proportional to the square root of current. The current noise magnitude is usually expressed by a noise index given as the ratio of the root-mean-square current noise voltage (ERMS) FIGURE 1.7 Typical graph of impedance as a percentage of dc resistance versus frequency for film resistors. Voltage coefficient = 100( ( 1 2 1 R R R V V – ) – ) 2 2 E kRT f RMS = 4 D