Основы измерений. Долгополов В.Т. - 46 стр.

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МФТИ | Москва

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20. Pbnjh – ZgZeh]h\h_ ij_h[jZah\Zgb_.
Pbnjh – ZgZeh]h\h_ ij_h[jZah\Zgb_ k\h^blky d ihkljh_gbx gZijy`_gby,
ijhihjpbhgZevgh]h qbkem, aZ^Zgghfm \ ^\hbqghf dh^_. JZkkfhljbf ijhkl_crmx
j_ZebaZpbx lZdh]h ij_h[jZah\Zl_ey. Imklv pbnjh\hc kb]gZe aZ^Zg n+1 [blZfb.
D = ( a
n
a
n-1
…..a
1
a
0
)
GZf lj_[m_lky ihkljhblv gZijy`_gb_ V = V
0
6 a
i
2
i
. IjbgpbibZevgh ih^h[gh_
ij_h[jZah\Zgb_ fh`_l [ulv \uiheg_gh k ihfhsvx ko_fu, bah[jZ`_gghc gZ Jbk.52.
Khijhlb\e_gby R
i
^he`gu [ulv ih^h[jZgu lZdbf h[jZahf, qlh R
i
= 2 R
i+1
. Dexqb
^he`gu jZ[hlZlv lZdbf h[jZahf, qlh ijb _^bgbp_ \ khhl\_lkl\mxs_f jZajy^_ j_abklhj
ih^dexq_g d bklhqgbdm hihjgh]h gZijy`_gby, Z ijb gme_ –khijhlb\e_gb_ ih^dexqZ_lky d
a_fe_. Ihkdhevdm Hm jZ[hlZ_l \ j_`bf_ dhg\_jl_jZ lhd- gZijy`_gb_, lh bg\_jlbjmxsbc
\oh^ y\ey_lky \bjlmZevghc a_fe_c b gZijy`_gb_ gZ \uoh^_ jZ\gh
V
A
= (V
R
/R)*R
t
*6 a
i
2
i
GZijbf_j, ^ey j_ZebaZpbb ij_h[jZah\Zgby pbnjZ-ZgZeh] k lhqghklvx \ ljb agZdZ, fh`gh
bkihevah\Zlv R
0
=1 Fhf, R
10
=R
0
/1024, R
t
=1 Dhf.
<k_ dexqb kljhylky, _kl_kl\_ggh, we_dljhgguf h[jZahf. G_^hklZldhf
ij_^eh`_ggh]h ij_h[jZah\Zl_ey y\ey_lky g_h[oh^bfhklv lhqgh \u^_j`b\Zlv
khhlghr_gby f_`^m khijhlb\e_gbyfb. Hkh[_ggh lhqgufb ^he`gu [ulv khijhlb\e_gby
klZjrbo jZajy^h\.
Jbk. 52.
Ij_h[jZah\Zgb_ k ihfhsvx j_abklhjghc fZljbpu.
Jbk. 53. 
20. Pbnjh – ZgZeh]h\h_ ij_h[jZah\Zgb_.
       Pbnjh – ZgZeh]h\h_ ij_h[jZah\Zgb_ k\h^blky d ihkljh_gbx gZijy`_gby,
ijhihjpbhgZevgh]h qbkem, aZ^Zgghfm \ ^\hbqghf dh^_. JZkkfhljbf ijhkl_crmx
j_ZebaZpbx lZdh]h ij_h[jZah\Zl_ey. Imklv pbnjh\hc kb]gZe aZ^Zg n+1 [blZfb.
                                  D = ( an an-1…..a1 a0)
GZf lj_[m_lky ihkljhblv gZijy`_gb_ V = V0 6 ai2i. IjbgpbibZevgh ih^h[gh_
ij_h[jZah\Zgb_ fh`_l [ulv \uiheg_gh k ihfhsvx ko_fu, bah[jZ`_gghc gZ Jbk.52.
Khijhlb\e_gby Ri ^he`gu [ulv ih^h[jZgu lZdbf h[jZahf, qlh Ri = 2 Ri+1. Dexqb
^he`gu jZ[hlZlv lZdbf h[jZahf, qlh ijb _^bgbp_ \ khhl\_lkl\mxs_f jZajy^_ j_abklhj
ih^dexq_g d bklhqgbdm hihjgh]h gZijy`_gby, Z ijb gme_ –khijhlb\e_gb_ ih^dexqZ_lky d
a_fe_. Ihkdhevdm Hm jZ[hlZ_l \ j_`bf_ dhg\_jl_jZ lhd- gZijy`_gb_, lh bg\_jlbjmxsbc
\oh^ y\ey_lky \bjlmZevghc a_fe_c b gZijy`_gb_ gZ \uoh^_ jZ\gh
                                 VA = (VR/R)*Rt*6 ai2i
GZijbf_j, ^ey j_ZebaZpbb ij_h[jZah\Zgby pbnjZ-ZgZeh] k lhqghklvx \ ljb agZdZ, fh`gh
bkihevah\Zlv R0 =1 Fhf, R10 =R0/1024, Rt =1 Dhf.

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