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504 Antennas for low-frequency operation The basic foundation for these antennas is a very short vertical antenna The standard vertical antenna is a quarter-wavelength ( /4) (ie, 90 electrical length), and it is unbalanced with respect to ground Recall that a vertical antenna that is too short for its operating frequency (ie, less than /4) will exhibit capacitive reactance In order to resonate that antenna, it is necessary to cancel the capacitive reactance with an equivalent inductive reactance, such as XL = XC By placing an inductance in series with the antenna radiator element, therefore, we can effectively lengthen it electrically Of course, what is really happening is that the effects of the lower operating frequency are being accommodated (ie, cancelled out ) of a too-short antenna An antenna that is reactance-compensated for a different frequency is said to be loaded, or in the case of a very low frequency antenna, inductively loaded Three basic forms of loading are popular: discrete loading, continuous loading, and linear loading Discrete loading means that there is a discrete, or lumped, inductance in series with the antenna radiator (Figs 26-2A through 26-2C) These antennas are so constructed that a loading coil is placed at the center (Fig 26-2A), top (Fig 26-2B), or bottom (Fig 26-2C) of the radiator element You will recognize these configurations as being the same as those found on mobile antennas Indeed, low-band mobile antennas can be used in both mobile and fixed installations Note, however, that although it is convenient to use mobile antennas for fixed locations (because they are easily available in store bought form); they are less efficient than other versions of the same concept The reason is that the mobile antenna, for low frequencies, tends to be based on the standard 96- to 102-in whip antenna used by amateur operators on 10 m or Citizens Band operators on 11 m In fixed locations, on the other hand, longer radiator elements (which are more efficient) are more easily handled For example, a 16- to 30-ft high aluminum radiator element can easily be constructed of readily available materials The 16-ft element can be bought in the form of one or two lengths of 1- to 15-in aluminum tubing at do-it-yourself outlets A problem seen with these antennas is that they tend to be rather high Q, so the bandwidth is necessarily narrow An antenna might work in the center of a band, but present a high VSWR at the ends of the band, and thus be unusable This problem is solved by making the inductor variable so that slightly different inductance values can be selected at different frequencies across the band For the base-loaded version (Fig 26-2C), this is particularly easy: a rotary inductor (perhaps motor driven for remote operation) can be used For the other configurations, a tapped fixed inductor can be used instead Each tap represents a different inductance value Either clip connectors, or relay connections, can be used to select which tap is used A continuously loaded antenna has the inductance distributed along the entire length of the radiator (Fig 26-2D) Typical of these antennas is the helically wound verticals in which about a half-wavelength of insulated wire is wound over an insulating form (such as a length of PVC pipe or a wooden dowel); the turns of the coil are spread out over the entire length of the insulated support Linear loading (Fig 26-2E) is an arrangement whereby a section of the antenna is folded back on itself like a stub Antennas of this sort have been successfully.



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Rewrite 48 104 as 048 105 Group terms Add terms Round using addition/subtraction rule for significant digits

13 Evaluate each expression Express the result in scientific notation a (52 10

4 )(40

108 )

1 package com; 2 public class MyClass { 3 public static void howdy() { Systemoutprint("howdy "); } 4 public static final int myConstant = 343; 5 public static final MyClass mc = new MyClass(); 6 public int instVar = 42; 7 } 11 import comMyClass; 12 public class TestImports2 {

b (24 103 )

(80 104 )

Shortened horizontal antennas 505 built from the same type of aluminum tubing as regular verticals For 75/80-m (375-MHz) operation a length of 30 ft for the radiator represents 41 , while a normal /4 vertical is 90 The difference between 90 and 41 of electrical length is made up by the hairpin structure at the base





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Scientists and mathematicians have agreed on a set of steps or rules, called the order of operations, so that everyone interprets mathematical symbols in the same way Follow these steps in order when you evaluate an expression or use a formula 1 Simplify the expressions inside grouping symbols, like parentheses ( ), brackets [ ], braces { }, and fraction bars 2 Evaluate all powers and roots 3 Do all multiplications and/or divisions from left to right 4 Do all additions and/or subtractions from left to right Example: Simplify the following expression 4 3(4 1) 23 4 3(3) 23 4 3(3) 8 4 9 8 8

13 public static void main(String[] args) { 14 MyClasshowdy(); 15 Systemoutprint(MyClassmyConstant + " "); 16 Systemoutprint(myConstant + " "); 17 howdy(); 18 Systemoutprint(mcinstVar + " "); 19 Systemoutprint(instVar + " "); 20 } }

Order of operations step 1 Order of operations step 2 Order of operations step 3 Order of operations step 4

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Connecting Math to Physics The previous example was shown step-by-step to demonstrate order of operations When solving a physics problem, do not round to the correct number of siginificant digits until after the final calculation In calculations involving an expression in a numerator and an expression in a denominator, the numerator and the denominator are separate groups and are to be calculated before dividing the numerator by the denominator So, the multiplication/division rule is used to determine the final number of significant digits

15 102 10 103

You will describe momentum and impulse and apply them to the interactions between objects You will relate Newton s third law of motion to conservation of momentum You will explore the momentum of rotating objects

What is the result (Choose all that apply) A howdy 343 343 howdy 42 42 B Compilation fails due to an error on line 14 C Compilation fails due to an error on line 15 D Compilation fails due to an error on line 16 E Compilation fails due to an error on line 17 F Compilation fails due to an error on line 18 G Compilation fails due to an error on line 19 33 Given this code inside a method:

.

Momentum is the key to success in many sporting events, including baseball, football, ice hockey, and tennis Baseball Every baseball player dreams of hitting a home run When a player hits the ball, at the moment of collision, the ball and the bat are deformed by the collision The resulting change in momentum determines the batter s success

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