when working with dB in the voltage domain, we are working with the E2/R relationship, where R = 75 S2. With this in mind the definition of dBmV is (17.2) If a signal level is 1 V at a certain point in a circuit, what is the level in dBmV? dBmV = 20 log(1000/1) = +60 dBmV. If we are given a signal level of +6 dBmV, to what voltage level does this correspond? +6 dBmV = 20 log(Xmv/1mV). Divide through by 20: 6/20 = log(Xmv/1 mV) antilog(6/20) = Xmv Xmv = 1.995 mV, or 2 mV, or 0.002 V These signal voltages are rms (root mean square) volts. For peak voltage, divide by 0.707. If you are given peak signal voltage and wish the rms value, multiply by 0.707. 17.3.3 Thermal Noise in CATV Systems We remember from Section 3.3.3 that thermal noise is the most common type of noise encountered in telecommunication systems. In most cases, it is thermal noise that sets the sensitivity of a system, its lowest operating threshold. In the case of a CATV system, the lowest noise levels permissible are set by the thermal noise level-at the antenna output terminals, at repeater (amplifier) inputs, or at a subscriber's TV set-without producing snowy pictures. Consider the following, remembering we are in the voltage domain. Any resistor or source that looks resistive over the band of interest, including antennas, amplifiers, and long runs of coaxial cable, generates thermal noise. In the case of a resistor, the thermal noise level can be calculated based on Figure 17.3. To calculate the noise voltage, en, use the following formula: en = (4RBk)1/2, (17.3) where en = rms noise voltage, R = resistance in ohms (S2), B = bandwidth (Hz) of the measuring device (electronic voltmeter, V), and k = a constant equal to 40 X 10-16 at standard room temperature. 2 Figure 17.3 Resistor model for thermal noise voltage, en. This value can be derived from Boltzmann's constant (Chapter 3) at room temperature (68°F or 290 K) is assumed. COMMUNITY ANTENNA TELEVISION (CABLE TELEVISION) 2.2 uV Resistor 1.1 uV generating noise Figure 17.4 Minimum noise model. 