2011美国赛AB题目的原题及翻译

2011美国赛AB题目的原题及翻译
2011美国赛AB题目的原题及翻译

PROBLEM A: Snowboard Course

Determine the shape of a snowboard course (currently known as a “halfpipe”) to maximize the production of “vertical air” by a skilled snowboarder.

"Vertical air" is the maximum vertical distance above the edge of the halfpipe.

Tailor the shape to optimize other possible requirements, such as maximum twist in the air.

What tradeoffs may be required to develop a “practical” course?

A题:单板滑雪场地

请设计一个单板滑雪场(现为“半管”或“U型池”)的形状,以便能使熟练的单板滑雪选手最大限度地产生垂直腾空。

“垂直腾空“是超出“半管”边缘以上的最大的垂直距离。

定制形状时要优化其他可能的要求,如:在空中产生最大的身体扭转。

在制定一个“实用”的场地时哪些权衡因素可能需要?

PROBLEM B: Repeater Coordination

The VHF radio spectrum involves line-of-sight transmission and reception. This limitat ion can be overcome by “repeaters,” which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.

In addition to geographical separation, the “continuous tone-coded squelch system”(CTCSS), sometimes nicknamed “private line” (PL), technology can be used to mitigate interference problems. This system associates to each repeater a separate subaudible tone that is transmitted by all users who wish to communicate through that repeater. The repeater responds only to received signals with its specific PL tone. With this system, two nearby repeaters can share the same frequency pair (for receive and transmit); so more repeaters (and hence more users) can be accommodated in a particular area.

For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available.

How does your solution change if there are 10,000 users?

Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.

B题中继站的协调

甚高频无线电频谱包含信号的发送和接受。这种限制可以被中继站所克服。中继站可以捕捉到微弱的信号,然后把它放大,再用不同的频率重新发送。这样,低功耗的用户,例如移动电话用户,在不能直接与其他用户联系的地方可以通过中继站来保持联系。

重点:然而,中继站之间会互相影响,除非彼此之间有足够远的距离或通过充分分离的频率来传送。(中继站之间距离太近,会使接收机收到的信号太强以至于LNA处于饱和状态,工作异常。)

除了地理的分离、“连续编码音调控制系统”(CTCSS),有时被称为“私人专线”(PL)( 最常用的亚音就是CTCSS(Continuous Tone Coded SquelchSystem),直接翻译就是连续音频编码静噪系统,Motorola称为PL,是属于模拟亚音,频率从67.0Hz、69.3Hz、一直到250.3Hz,共39个亚音点(或50个点)。)、通过这项技术可以减轻干扰问题。该系统连接每个中继站,靠的是所有通过同一个中继站连接的用户发送的独立的亚音频音调来连接。中继站只回应接收到的具有特殊PL(Private Line Codes)的语调的信号。(尽管说是亚音,但事实上是可以听到的,尤其是把亚音设置在高限(250Hz附近),或者接收机的低频频响比较好的时候。因此,我们设置亚音的时候,都尽量设置的低一些,以免不必要的干扰。)通过这个系统,两个附近的中继站可以共享相同的频率对(包括接收和发送);对于更多的中继站(并且更多的用户)可以提供在一个特定的区域。

(1)在一个半径40英里的圆形区域,请你设计一个方案,用最少量的中继站来容纳1000同时在线用户。假设频谱范围是145到148兆赫(频道间隔为25KHz,意味着只有120个频道可用),在中继站中的发射机的频率要么是高于接收机频率600千赫,要么低于接收机频率600千赫、并且这里有54个不同的PL可用。(这道题目我是这样理解的~54个亚音频相当于54种不同颜色的帽子~然后就相当于给每个传输中的信号带了帽子~

然后每个中继器只能接一个特定颜色的帽子~可以传出别的颜色的帽子的给别的中继器~

本来假如信号按频率分总共有84种信号~再给每个频率的信号带帽子,可以带成84种样子~所以就可以相当于信号总的分成84*54种了)

(2)如果这里有10,000个用户,如何改变你的解决方案。

(3)在由于山区引起信号传播的阻碍的地区,讨论这样的情形。

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