⚡ Transponder Saturation & HPA Backoff Calculator

TWTA / SSPA saturation curve — IBO/OBO conversion, gain compression & multicarrier intermodulation

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Amplifier

Operating Point

Third-order intermodulation reference (optional) — a known C/I₃ point from a datasheet or measurement: 三阶互调参考点(可选)——来自数据表或实测的已知 C/I₃ 数据点:

Results

Input Backoff (IBO)
– dB
Output Backoff (OBO)
– dB
Gain compression
– dB
Total output power
– dBW
Per-carrier output power
– dBW
Estimated C/I₃
– dB
Show full breakdown

Saturation Curve (AM/AM)

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📖 How to use

  1. Pick a preset, or choose the amplifier type: TWTA (smooth gain roll-off, can be over-driven past saturation) or SSPA (Rapp model, tune the smoothness factor p — higher p = sharper, more limiter-like knee). 选择一个预设,或设置放大器类型:TWTA(增益平滑滚降,可过驱动越过饱和点)或 SSPA(Rapp 模型,调节平滑因子 p——p 越大,膝点越陡、越接近硬限幅)。
  2. Enter the saturated output power Psat and small-signal gain G₀ (G₀ only affects the reported drive power, not the backoff numbers). 输入饱和输出功率 Psat 和小信号增益 G₀(G₀ 只影响所报告的驱动功率,不影响回退数值本身)。
  3. Choose whether you're setting IBO or OBO and enter the value — the other one is computed from the saturation curve, along with gain compression. 选择你要设定的是 IBO 还是 OBO 并填入数值——另一个值及增益压缩会按饱和曲线自动算出。
  4. Set carriers (FDMA) if several equal-power carriers share this HPA — backoff above is the total/composite value; per-carrier figures divide the power by N. 如果多个等功率载波共用同一只 HPA,填写载波数(FDMA)——上面的回退是总/合成值;各载波数值按 N 等分功率得到。
  5. Optionally calibrate the C/I₃ reference with a known datasheet or measured point; the tool converts that point's OBO to an IBO through the saturation curve, then extrapolates using the standard 2 dB-per-dB small-signal slope in input backoff. This is approximate and breaks down near saturation. 可选地用数据表或实测的已知点校准C/I₃ 参考值;工具会先按饱和曲线把该点的 OBO 折算成 IBO,再按标准的小信号 2 dB/dB 斜率在输入回退上外推。该估算仅为近似,在接近饱和时会失准。
  6. Arrived via a ↗ link from the Link Budget? The return bar at the top carries the per-carrier output power back when you came from a Tx-power field, or the estimated C/I₃ when you came from an interference field (no bar appears on a direct visit). 如果是点链路预算里的 ↗ 链接跳转而来,顶部返回条会按来源字段带回对应值:从发射功率字段跳来带回每载波输出功率,从干扰字段跳来带回估算的 C/I₃(直接访问不会显示返回条)。

Why HPAs need backoff

A satellite HPA — a TWTA or SSPA — is linear only at low drive levels. As input power rises toward saturation (Psat), the gain compresses and the output-vs-input curve bends over. Operating with Input Backoff (IBO) and Output Backoff (OBO) — dB below the saturation input/output reference — trades away some output power and EIRP in exchange for linearity, which controls gain compression and limits the intermodulation products generated when several carriers (FDMA) share one amplifier.

Models used

TWTA — Saleh model (Saleh, 1981), normalised so the output reaches exactly Psat at the saturation input reference and rolls over if over-driven, as real TWTs do:

P_out/P_sat = 4ρ / (1+ρ)²,   ρ = P_in / P_in,sat

SSPA — Rapp model (Rapp, 1991), a smooth, monotonic soft limiter that never turns over — a good fit for solid-state amplifiers and for OFDM/multicarrier nonlinearity studies:

P_out/P_sat = u / (1+up)1/p,   u = P_in / P_in,sat

where p is the knee "smoothness" factor (larger p → sharper knee, approaching an ideal limiter). Both formulas are closed-form and invertible, so the calculator converts directly between IBO and OBO without iteration. Gain compression is the operating-point gain minus the small-signal gain G₀ — always ≤ 0 dB for a real compressive amplifier.

Multicarrier (FDMA) backoff

The backoff entered above is the total/composite value seen by the amplifier (the sum of all carriers). For N equal-power carriers, the per-carrier backoff referenced to a single carrier driving the amp alone is IBO_carrier = IBO_total + 10·log₁₀(N) (and likewise for OBO) — adding carriers effectively pushes the amplifier closer to saturation for the same per-carrier power, which is exactly why multicarrier transponders need more backoff than a single-carrier one.

Third-order intermodulation (C/I₃)

Near saturation, intermodulation products (IM3) generated by two or more carriers in the same HPA can fall back into the desired channels. In the weakly-nonlinear (well-backed-off) regime, a cubic nonlinearity makes the fundamental output grow 1 dB per dB of drive while IM3 grows 3 dB per dB of drive — so C/I₃ improves by 2 dB for every extra dB of input backoff. The slope is per dB of drive, so it applies to IBO, not OBO: the reference (C/I₃, OBO) point you supply (e.g. from a manufacturer's curve) is first carried back through the AM/AM curve above to its equivalent IBO, and the extrapolation runs from there. Once the amplifier is compressed a dB of OBO is worth much more than a dB of IBO, so working the slope directly in OBO would report an optimistic C/I₃. It is only an approximation either way: the real curve flattens out near saturation, where gain compression itself limits how bad IM3 can get.

Feed the resulting output power into the link budget's transmit power / EIRP. All computation runs locally in your browser.

为什么 HPA 需要回退(backoff)

卫星功放(HPA)——无论是 TWTA 还是 SSPA——只在低驱动电平下近似线性。当输入功率逼近饱和点(Psat)时,增益被压缩,输出-输入曲线发生弯曲。以输入回退(IBO)与输出回退(OBO)——相对饱和输入/输出参考点的 dB 值——运行,是用部分输出功率与 EIRP 换取线性度,从而控制增益压缩,并限制多载波(FDMA)共用一只功放时产生的互调产物。

使用的模型

TWTA——Saleh 模型(Saleh, 1981),归一化后输出在饱和输入参考点恰好达到 Psat,过驱动时会像真实 TWT 一样回落:

P_out/P_sat = 4ρ / (1+ρ)²,  ρ = P_in / P_in,sat

SSPA——Rapp 模型(Rapp, 1991),平滑、单调的软限幅器,永不回落——适合固态放大器以及 OFDM/多载波非线性研究:

P_out/P_sat = u / (1+up)1/p,  u = P_in / P_in,sat

其中 p 为膝点"平滑度"因子(p 越大→膝点越陡,趋近理想限幅器)。两个公式都是闭式且可逆的,因此计算器无需迭代即可在 IBO 与 OBO 之间直接换算。增益压缩为工作点增益减去小信号增益 G₀——对真实的压缩型放大器恒 ≤ 0 dB。

多载波(FDMA)回退

上面填入的回退是放大器看到的总/合成值(所有载波之和)。对于 N 个等功率载波,折算到"单一载波单独驱动该功放"的单载波回退为 IBO_单载波 = IBO_总 + 10·log₁₀(N)(OBO 同理)——增加载波数会在相同单载波功率下使放大器更接近饱和,这正是多载波转发器比单载波需要更多回退的原因。

三阶互调(C/I₃)

接近饱和时,同一只 HPA 中两个或更多载波产生的互调产物(IM3)可能落回有用信道。在弱非线性(回退较深)区域,三次项非线性使基波输出每 dB 驱动增长 1 dB,而 IM3 每 dB 驱动增长 3 dB——因此每多 1 dB 输入回退,C/I₃ 改善 2 dB。该斜率是相对驱动电平而言的,因此作用对象是 IBO 而非 OBO:你提供的参考点(C/I₃、OBO)会先经上面的 AM/AM 曲线折算回等效 IBO,再从该点外推。放大器一旦进入压缩区,1 dB 的 OBO 远比 1 dB 的 IBO "值钱",若直接按 OBO 套用该斜率会把 C/I₃ 算得过于乐观。无论如何这只是近似:实际曲线在接近饱和时会变平,因为增益压缩本身限制了 IM3 能恶化到多严重。

将得到的输出功率代入链路预算的发射功率 / EIRP。全部计算在你的浏览器本地完成。