Antenna Efficiency Calculator Antenna Efficiency Calculator Calculate the antenna efficiency using the formula: \[ \eta = \frac{R_r}{R_r + R_l} \times 100\% \] * Enter the radiation resistance \( R_r \) (Ω) and loss resistance \( R_l \) (Ω). Step 1: Enter Parameters Radiation Resistance, \( R_r \) (Ω): Example: 50 Ω Loss Resistance, \( R_l […]
Radar Range Calculator Radar Range Calculator Calculate the maximum radar range using the radar range equation: \[ R = \left( \frac{P_t\,G^2\,\lambda^2\,\sigma}{(4\pi)^3\,S_{\min}} \right)^{\frac{1}{4}} \] * Enter the transmitted power \(P_t\) (W), antenna gain \(G\), wavelength \(\lambda\) (m), radar cross-section \(\sigma\) (m²), and minimum detectable signal \(S_{\min}\) (W). Step 1: Enter Parameters Transmitted Power, \( P_t \) […]
Gamma Function Calculator Gamma Function Calculator Calculate the Gamma function using the formula: \[ \Gamma(z) = \int_0^\infty t^{z-1} e^{-t}\, dt = \frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \quad (\text{for related Beta functions}) \] (Here, we use the Lanczos approximation for \(\Gamma(z)\).) * Enter a positive value for \( z \). Step 1: Enter Parameter Value \( z \): Example: 2.5 […]
Beta Function Calculator Beta Function Calculator Calculate the Beta function using the formula: \[ B(x,y) = \frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \] * Enter positive values for \( x \) and \( y \). Step 1: Enter Parameters x: Example: 2 y: Example: 3 Calculate Beta Function Calculated Beta Function Recalculate Formula: \( B(x,y) = \frac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \) Practical Example: […]
Parabolic Projectile from an Elevation Calculator Parabolic Projectile from an Elevation Calculator Enter the initial velocity \(v_0\) (m/s), launch angle \(\theta\) (°), and initial elevation \(h_0\) (m) to calculate: Time of Flight: \[ T = \frac{v_0\sin\theta + \sqrt{(v_0\sin\theta)^2 + 2g\,h_0}}{g} \] Horizontal Range: \[ R = v_0\cos\theta\,T \] Maximum Height (relative to ground): \[ H_{max} […]
Projectile on an Incline (Downward Motion) Calculator Projectile on an Incline (Downward Motion) Calculator Calculate the key parameters for a projectile launched downward on an inclined plane. Equations used: Time of Flight: \[ t = \frac{2\,v_0\,\sin\left(\phi-\theta\right)}{g\,\cos\phi} \] Range along the Incline: \[ R = \frac{2\,v_0^2\,\cos\theta\,\sin\left(\phi-\theta\right)}{g\,\cos^2\phi} \] * Enter the initial velocity (m/s), launch angle (°), […]
Projectile on an Incline (Upward Motion) Calculator Projectile on an Incline (Upward Motion) Calculator Calculate the key parameters for a projectile launched upward on an inclined plane. The equations used are: Time of Flight: \[ t = \frac{2\,v_0\,\sin\left(\theta-\phi\right)}{g\,\cos\phi} \] Range along the Incline: \[ R = \frac{2\,v_0^2\,\sin\left(\theta-\phi\right)\cos\theta}{g\,\cos^2\phi} \] Maximum Height above the Incline: \[ H_{max} […]
Projectile on an Incline (Downward Motion) Calculator Projectile on an Incline (Downward Motion) Calculator Calculate key parameters for a projectile launched downward on an incline (with the projectile moving downward relative to the plane). The equations used are: Time of Flight: \[ t = \frac{2\,v_0\,\sin\left(\phi-\theta\right)}{g\,\cos\phi} \] Range along the Incline: \[ R = \frac{2\,v_0^2\,\cos\theta\,\sin\left(\phi-\theta\right)}{g\,\cos^2\phi} \] […]
Projectile on an Incline Calculator Projectile on an Incline Calculator Calculate key parameters for a projectile launched on an incline (with the projectile moving upward relative to the plane). The equations used are: Time of Flight: \[ t = \frac{2\,v_0\,\sin\left(\theta-\phi\right)}{g\,\cos\phi} \] Range along the incline: \[ R = \frac{2\,v_0^2\,\cos\theta\,\sin\left(\theta-\phi\right)}{g\,\cos^2\phi} \] Maximum height above the incline: […]
V₍CE(sat)₎ Calculator Using Ebers–Moll Model for a BJT V₍CE(sat)₎ Calculator Using Ebers–Moll Model Calculate the collector–emitter saturation voltage using the simplified Ebers–Moll model: \[ V_{CE(sat)} \approx V_T \ln\left(\frac{I_{CS}}{\alpha_F\,I_{ES}}\right) \] where \(V_T\) is the thermal voltage, \(I_{ES}\) is the emitter saturation current, \(I_{CS}\) is the collector saturation current, and \(\alpha_F\) is the forward common‐base current gain. […]