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$$-N=\overline{N}+1$$

$$-2^{n-1}\le N\le 2^{n-1}-1$$

$$2^p\ge m+p+1$$

$$g_i=b_{i+1}\oplus b_i,g_{n-1}=b_{n-1}$$

$$b_i=b_{i+1}\oplus g_i$$

$$\overline{A+B}=\overline{A}\overline{B},\overline{AB}=\overline{A}+\overline{B}$$

$$A+AB=A,A+\overline{A}B=A+B$$

$$AB+\overline{A}C+BC=AB+\overline{A}C$$

$$A\oplus B=A\overline{B}+\overline{A}B$$

$$A\odot B=AB+\overline{A}\overline{B}$$

$$N=\min \left(\frac{I_{OL}}{I_{IL}},\frac{I_{OH}}{I_{IH}}\right)$$

$$N{M}_H=V_{OH}-V_{IH},N{M}_L=V_{IL}-V_{OL}$$

$$t_{pd}=\frac{t_{PHL}+t_{PLH}}{2}$$

$$P=C{V}_{DD}^{2}f$$

$$S=A\oplus B\oplus C_{in}$$

$$C_{out}=AB+C_{in}(A\oplus B)$$

$$C_{i+1}=G_i+P_i{C}_i$$

$$2^n=\text{입력 수}$$

$$Q^{+}=J\overline{Q}+\overline{K}Q$$

$$Q^{+}=T\oplus Q$$

$$Q^{+}=S+\overline{R}Q,SR=0$$

$$Q^{+}=D$$

$$n=\lceil {\log }_{2}N\rceil$$

$$f_{max}=\frac{1}{n{t}_{pd}}$$

$$f_{out}=f_{in}/2^n$$

$$2n$$

$$\%=\frac{1}{2^n-1}\times 100$$

$$1\text{LSB}=\frac{V_{FS}}{2^n}\text{또는}\frac{V_{FS}}{2^n-1}$$

$$2^n-1$$

$$f_s\ge 2f_{max}$$

$$SQNR\approx 6.02n+1.76\text{dB}$$

$$C=2^a\times d\text{[bit]}$$

$$T=h{t}_c+(1-h)t_m$$

$$\Delta V=\frac{V_{ref}}{2^n}$$

$$V_{avg}=D\cdot V_H$$

$$V_{avg}=V_m/\pi$$

$$V_{avg}=2V_m/\pi$$

$$\gamma =\frac{V_{r,rms}}{V_{DC}}=\sqrt{F^2-1}$$

$$V_{r(pp)}\approx \frac{I_{DC}}{f_{r}C}$$

$$I_Z=\frac{V_{in}-V_Z}{R_S}-\frac{V_Z}{R_L}$$

$$r_d=\frac{26\text{mV}}{I_D}$$

$$\beta =\frac{\alpha }{1-\alpha }$$

$$\alpha =\frac{\beta }{1+\beta }$$

$$I_B=\frac{V_{CC}-V_{BE}}{R_B},V_{CE}=V_{CC}-I_C{R}_C$$

$$V_B=V_{CC}\frac{R_2}{R_1+R_2},I_E=\frac{V_B-V_{BE}}{R_E}$$

$$S=1+\beta$$

$$r_e=\frac{26\text{mV}}{I_E}$$

$$A_v\approx -\frac{R_C\parallel R_L}{r_e}$$

$$A_v\approx -\frac{R_C}{r_e+R_E}$$

$$Z_{in}\approx \beta (r_e+R_E)$$

$${\beta }_D\approx {\beta }_1{\beta }_2$$

$$I_D=I_{DSS}{\left(1-\frac{V_{GS}}{V_P}\right)}^2$$

$$g_{m0}=\frac{2I_{DSS}}{|V_P|}$$

$$g_m=g_{m0}\left(1-\frac{V_{GS}}{V_P}\right)$$

$$I_D=k(V_{GS}-V_T{)}^2$$

$$A_v=-g_m{R}_D$$

$$G=20{\log }_{10}{A}_v$$

$$G=10{\log }_{10}{A}_p$$

$$C_M=C_f(1+|A_v|)$$

$$f_T\approx \beta f_{\beta }$$

$$f_H^{\ast }=f_H\sqrt{2^{1/n}-1}$$

$$A\cdot BW=GBW$$

$$A_f=\frac{A}{1+A\beta }$$

$$B{W}_f=BW(1+A\beta )$$

$$\frac{d{A}_f}{A_f}=\frac{1}{1+A\beta }\frac{dA}{A}$$

$$F=20\log (1+A\beta )\text{dB}$$

$$A_v=-\frac{R_f}{R_1}$$

$$A_v=1+\frac{R_f}{R_1}$$

$$V_o=-\frac{1}{RC}\int V_{i}dt$$

$$V_o=-RC\frac{d{V}_i}{dt}$$

$$CMRR=20\log \frac{A_d}{A_c}$$

$$f_{max}=\frac{SR}{2\pi V_m}$$

$$A\beta =1\angle 0^{\circ }$$

$$f=\frac{1}{2\pi RC}$$

$$f=\frac{1}{2\pi \sqrt{6}RC}$$

$$f=\frac{1}{2\pi \sqrt{L\frac{C_1{C}_2}{C_1+C_2}}}$$

$$f=\frac{1}{2\pi \sqrt{(L_1+L_2+2M)C}}$$

$${\eta }_{max}=\frac{\pi }{4}=78.5\%$$

$$\epsilon =\frac{V_{NL}-V_{FL}}{V_{FL}}\times 100$$

$$V_o=D{V}_{in}$$

$$V_o=\frac{V_{in}}{1-D}$$

$$V_o=-\frac{D}{1-D}{V}_{in}$$

$$m=\frac{V_{max}-V_{min}}{V_{max}+V_{min}}$$

$$P_t=P_c\left(1+\frac{m^2}{2}\right)$$

$$m_f=\frac{\Delta f}{f_m}$$

$$B=2(\Delta f+f_m)$$

$$f=\frac{1.44}{(R_A+2R_B)C}$$

$$f_{img}=f_s+2f_{IF}$$

$$R=\frac{R_1{R}_2}{R_1+R_2}$$

$$V_2=V\frac{R_2}{R_1+R_2}$$

$$I_1=I\frac{R_2}{R_1+R_2}$$

$$P_{max}=\frac{V_{th}^2}{4R_{th}}$$

$$R_2=R_1\{1+\alpha (t_2-t_1)\}$$

$$V=\frac{\sum E_k/R_k}{\sum 1/R_k}$$

$$V=\frac{V_m}{\sqrt{2}}$$

$$X_L=2\pi fL$$

$$X_C=\frac{1}{2\pi fC}$$

$$|Z|=\sqrt{R^2+(X_L-X_C{)}^2}$$

$$\cos \theta =\frac{R}{|Z|}=\frac{P}{S}$$

$$P=\sqrt{3}{V}_l{I}_l\cos \theta$$

$$f_0=\frac{1}{2\pi \sqrt{LC}}$$

$$Q=\frac{1}{R}\sqrt{\frac{L}{C}}$$

$$B=\frac{f_0}{Q}$$

$$f_c=\frac{1}{2\pi RC}$$

$$f_c=\frac{R}{2\pi L}$$

$$\tau =RC$$

$$\tau =\frac{L}{R}$$

$$v_C=V(1-e^{-t/\tau })$$

$$v_C=V{e}^{-t/\tau }$$

$$R^2<\frac{4L}{C}$$

$$F=9\times 10^9\frac{Q_1{Q}_2}{r^2}$$

$$C=\epsilon \frac{S}{d}$$

$$W=\frac{1}{2}C{V}^2$$

$$H=\frac{I}{2\pi r}$$

$$F=BIl\sin \theta$$

$$e=-N\frac{d\Phi }{dt}$$

$$M=k\sqrt{L_1{L}_2}$$

$$W=\frac{1}{2}L{I}^2$$

$$R=(10a+b)\times 10^c$$

$$C=(10a+b)\times 10^c\text{pF}$$

$$1\text{mil}=0.0254\text{mm}$$

$$1\text{oz}\approx 35\mu \text{m}$$

$$R(t)=e^{-\lambda t}$$

$$MTBF=\frac{1}{\lambda }$$

$$R_s=1-\prod (1-R_i)$$

$$A=\frac{MTBF}{MTBF+MTTR}$$

$$V_n=\sqrt{4kTRB}$$

$$F=F_1+\frac{F_2-1}{G_1}+\cdots$$

$${\epsilon }_r=\frac{M-T}{T}\times 100$$

$${\alpha }_r=\frac{T-M}{M}\times 100$$

$$\Delta =\text{최대 눈금}\times \frac{\text{등급}}{100}$$

$$R_s=\frac{R_a}{m-1}$$

$$R_m=R_v(m-1)$$

$$R=\text{감도}[\Omega /V]\times \text{레인지}[V]$$

$$PR=QX\Rightarrow X=\frac{P}{Q}R$$

$$Z_1{Z}_4=Z_2{Z}_3$$

$$Q=\frac{V_C}{V}$$

$$f=\frac{1}{(\text{s/div})\times \text{div}}$$

$$\frac{f_y}{f_x}=\frac{n_{수평}}{n_{수직}}$$

$$\sin \theta =\frac{b}{a}$$

$$t_r=\frac{0.35}{BW}$$

$$t_m=\sqrt{t_s^2+t_o^2}$$

$$\Delta f=\frac{1}{T_{gate}}$$

$$THD=\frac{\sqrt{{\sum }_{n\ge 2}{V}_n^2}}{V_1}\times 100$$

$$P_{dBm}=10\log \frac{P}{1\text{mW}}$$

$$\Gamma =\frac{Z_L-Z_0}{Z_L+Z_0}$$

$$S=\frac{1+|\Gamma |}{1-|\Gamma |}$$

$$P=\frac{1}{2R}(V_3^2-V_1^2-V_2^2)$$

$$P=\frac{R}{2}(I_3^2-I_1^2-I_2^2)$$

$$P=W_1+W_2,Q=\sqrt{3}(W_1-W_2)$$

$$P=\frac{3600n}{Kt}\text{[kW]}$$

$$K=\frac{\Delta R/R}{\epsilon }$$

$$R_T=100(1+0.00385T)$$

$$V_H=\frac{R_{H}IB}{d}$$